jacobcd52/hs_math_cleaned · Datasets at Hugging Face

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the pattern below. 1, 3, 7, 13, 21, … 15. In △XYZ, ∠X and ∠Z are remote interior angles of exterior ∠XYT. If m∠X = (x + 15) °, m∠Z = (50 - 3x) °, and m∠XYT = (4x - 25) °, what is the value of x? 16. In △ABC and △DEF, ∠A ≅ ∠F. If EF = 4.5, DF = 3, ̶̶ AB would let you and AC = 1.5, what length for conclude that △ABC ∼ △...
–8 581 581 �� T E X A S TAKS Grades 9–11 Obj. 10 �� Reunion Tower The 55-story Reunion Tower is one of the most recognized buildings in the Dallas skyline. Built as a part of the Hyatt Regency Hotel, the tower is topped by a geodesic dome that houses a revolving ...
Choose one or more strategies to solve each problem. 1. In 1973, the National Park Service finished restoring President Johnson’s house to its appearance during Johnson’s childhood. The blueprint below shows the layout of the house after the restoration. Suppose there is a border of wallpaper along the edge of the cei...
m 7. 6 in. = ft 8. 15 m = mm Metric 1 kilometer = 1000 meters 1 meter = 100 centimeters 1 centimeter = 10 millimeters Customary 1 mile = 1760 yards 1 mile = 5280 feet 1 yard = 3 feet 1 foot = 12 inches Pythagorean Theorem Find x in each right triangle. Round to the nearest tenth, if necessary. 9. 11. 10. Measure with ...
2 Geo. Lab Les. 9-2 Les. 9-3 9-3 Geo. Lab Les. 9-4 Les. 9-5 Les. 9-6 9-6 Geo. Lab G.5.A Geometric patterns* use... geometric patterns to develop ★ ★ ★ algebraic expressions representing geometric properties G.5.B Geometric patterns* use... geometric patterns to make generalizations about geometric properties, including...
have already studied, and make flash cards of the formulas or theorems from the lesson. 2. Review your flash cards by looking at the front of each card and trying to recall the information on the back of the card. Extending Perimeter, Circumference, and Area 587 587 �� Literal Equations Algebra A literal equ...
a in terms of b and c, and use it to complete the following table. a b 48 36 14 c 35 36 50 588 588 Chapter 9 Extending Perimeter, Circumference, and Area �� 9-1 Developing Formulas for Triangles and Quadrilaterals TEKS G.5.A Geometric patterns: use... geometric patterns to develop algebraic expressions represent...
which b = 5 cm and A = (5 x 2 - 5x) cm 2 A = bh 5 x 2 - 5x = 5h 5 ( x 2 - x) = 5h x 2 - x = h Area of a rectangle Substitute 5 x 2 - 5x for A and 5 for b. Factor 5 out of the expression for A. Divide both sides by 5. h = ( x 2 - x) cm Sym. Prop. of = C the perimeter of the rectangle, in which A = 12 x ft 2 Step 1 Use ...
measurement. B the base of the triangle, in which A = x 2 in 2 bx bh 2x = b b = 2x in. Area of a triangle Substitute x 2 for A and x for h. Divide both sides by x. Multiply both sides by 2. Sym. Prop. of = C Area of a trapezoid b 2 of the trapezoid, in which A = 8 ft 3 + b 2 ) (2 ft Sym. Prop. of = Substitute 8 for A,...
x = 40 9 2 + y 2 = 15 2 y 2 = 144 y = 12 Step 2 Use d 1 and d 2 to find the area. d 1 is equal to x + y, which is 52. Half of d 2 is equal to 9, so d 2 is equal to 1852) (18) 2 A = 468 ft 2 Substitute 52 for d 1 and 18 for d 2. Area of a kite Simplify. 3. Find d 2 of a rhombus in which d 1 = 3x m and A = 12xy Games Ap...
triangle, in which p. 590 A = 58.5 in 2 6. b 1 of a trapezoid in which A = (48x + 68) in 2, h = 8 in., and b 2 = (9x + 12) in. the area of the rhombus p. 591 8. d 2 of the kite, in which A = 187.5 m 2 9. d 2 of a kite in which A = 12 x 2 y 3 cm 2, d 1 = 3xy cm 10. Art The stained-glass window shown is a rectangle p. 5...
�AEJ 22. trapezoid ABFJ � � � � � � � � � Multi-Step Find the area of each figure. Round to the nearest tenth, if necessary. 23. 24. 25. Write each area in terms of x. 26. equilateral triangle 27. 30°-60°-90° triangle 28. 45°-45°-90° triangle 594 594 Chapter 9 Extending Perimeter, Circumference, and Area ��...
12 in. President James Garfield was a classics professor and a major general in the Union Army. He was assassinated in 1881. Source: www.whitehouse.gov 43. The following proof of the Pythagorean Theorem was discovered by President James Garfield in 1876 while he was a member of the House of Representatives. a. Write t...
51. Write About It A square is also a parallelogram, a rectangle, and a rhombus. Prove that the area formula for each shape gives the same result as the formula for the area of a square. 52. Which expression best represents the area of the rectangle? 2x + 2 (x - c) x (x - c) x 2 + (x - c) 2 2x (x - c) 53. The length o...
lengths of the rectangle. Solve the perimeter formula 2x + 2y = 24 for y, and substitute the expression into the area formula A = xy. b. Graph the resulting function on a coordinate plane. What are the domain and range of the function? c. What are the dimensions of the rectangle that will enclose the greatest area? d....
possible. How could you use this π measuring tape to find the diameter of a circular object? Use your π measuring tape to measure 5 circular objects. Give the circumference and diameter of each object. 598 598 Chapter 9 Extending Perimeter, Circumference, and Area Archimedes used inscribed and circumscribed polygons t...
of a regular polygon apothem central angle of a regular polygon Who uses this? Drummers use drums of different sizes to produce different notes. The pitch is related to the area of the top of the drum. (See Example 2.) A circle is the locus of points in a plane that are a fixed distance from a point called the center ...
the circumference. C = 2πr C = 2π (3x) Substitute 3x for r. C = 6xπ cm Simplify. 1. Find the area of ⊙A in terms of π in which C = (4x - 6) π m. E X A M P L E 2 Music Application A drum kit contains three drums with diameters of 10 in., 12 in., and 14 in. Find the area of the top of each drum. Round to the nearest ten...
° Triangle Theorem, the apothem is 3 √  3 m3 √  3 ) (36) 2 aP Area of a regular polygon Substitute 3 √  3 for a and 36 for P. The tangent of an angle in a right triangle is the ratio of the opposite leg length to the adjacent leg length. See page 525. A = 54 √  3 ≅ 93.5 m 2 Simplify. B a regular pentagon with side ...
pizzas with diameters of 8 in., 10 in., and 12 in. p. 601 Find the area of each size pizza. Round to the nearest tenth Find the area of each regular polygon. Round to the nearest tenth. p. 602 6. 7. Independent Practice For See Exercises Example 10–12 13 14–17 1 2 3 TEKS TEKS TAKS TAKS Skills Practice p. S20 Applicati...
circumference of 2π in. Which calculation of the area is incorrect? Explain. Find the missing measurements for each circle. Give your answers in terms of π. Diameter d Radius r Area A Circumference C 6 34. 35. 36. 37. 100 17 36 π 38. Multi-Step Janet is designing a garden around a gazebo that is a regular hexagon with...
the table top that includes a 2-foot-by-1-foot rectangle and 4 squares with sides 0.5 foot long. Which information makes this scenario impossible? There will be no room left on the tabletop after the rectangle has been painted. A 2-foot-long rectangle will not fit on the circular tabletop. Squares cannot be painted on...
necessary. A B Divide the figure into rectangles. Divide the figure into parts. The base of the triangle is √  10. 2 2 - 4. 8 2 = 9 ft. area of top rectangle: A = bh = 12 (15) = 180 c m 2 area of bottom rectangle: A = bh = 9 (27) = 243 c m 2 shaded area: 180 + 243 = 423 c m 2 area of triangle: A = 1 __ 2 bh = 1 _...
A newly planted xeriscape uses 17 gallons of water per square foot per year. How much water will the garden require in one year? To find the area of the garden in square feet, divide the garden into parts. The area of the top rectangle is 28.5 (7.5) = 213.75 f t 2. The area of the center trapezoid is 1 __ 2 (12 + 18) ...
+ 3 + 2.5 + 1 = 8 cm 2 The shaded area is about 8 c m 2. 4. Use a composite figure to estimate the shaded area. The grid has squares with side lengths of 1 ft. THINK AND DISCUSS 1. Describe a composite figure whose area you could find by using subtraction. 2. Explain how to find the area of an irregular shape by using...
Give your answers in terms of π. 18. 19. 20. 21. Geography Use the grid on the map of Lake Superior to estimate the area of the surface of the lake. Each square on the grid has a side length of 100 miles. 22. Critical Thinking A trapezoid can be divided into a rectangle and two triangles. Show that the area formula fo...
each irregular shape and draw a composite figure that approximates it. Measure the composite figure and use it to estimate the area of the irregular shape. 28. 29. 30. Write About It Explain when you would use addition to find the area of a composite figure and when you would use subtraction. 31. Which equation can be...
What technical materials do you write? A: I write training manuals for computer software packages. Q: How do you use math? A: Some manuals I write are for math programs, so I use a lot of formulas to describe patterns and measurements. Q: What are your future plans? A: After I get a few more years experience writing m...
signs are usually made of reflective aluminum. A manufacturer of traffic signs begins with a rectangular sheet of aluminum that measures 60 in. by 90 in. 1. A railroad crossing sign is a circle with a diameter of 30 in. The manufacturer can make 6 of these signs from the sheet of aluminum by arranging the signs as sho...
15 �� 9-4 Perimeter and Area in the Coordinate Plane TEKS G.7.A Dimensionality and the geometry of location: use... two-dimensional coordinate systems to represent... figures. Also G.7.B, G.8.A Objective Find the perimeters and are...
m = See pages 44 and 182. Step 1 Draw the polygon. slope of Step 2 ABCD appears to be a rectangle. To verify this, use slopes to show that the sides are perpendicular. ̶̶ = 3 _ AB : - (-4) ̶̶ BC : 0 - 4 _ = -4 _ 4 - 2 2 ̶̶ = -3 _ CD : -3 - 0 _ = 1 _ -6 -2 - 4 2 1- (-3) = 4 _ _ -2 -4 - (-2) slope of slope of slope of ̶...
, -3), and Z (-4, 0). Draw the polygon and enclose it in a rectangle. area of the rectangle: A = bh = 8 (7) = 56 units 2 area of the triangles: bh = 1 _ a: A = 1 _ (5) (4) = 10 units 2 2 2 bh = 1 _ b: A = 1 _ (3) (2) = 3 units 2 2 2 bh = 1 _ c: A = 1 _ (2) (5) = 5 units 2 2 2 bh = 1 _ d: A = 1 _ (6) (3) = 9 units 2 2 2...
its 2 2 2 blue triangle: bh = 1 _ A = 1 _ (3) (1) = 1.5 u nits 2 2 2 green rectangle: A = bh = (3) (1) = 3 units 2 yellow rectangle: A = bh = (2) (1) = 2 units 2 yellow rectangle: A = bh = (2) (1) = 2 units 2 The areas are the same. Both figures have an area of 5 + 1.5 + 3 + 2 = 11.5 units 2. If the figures were triang...
(8, 1), S (-2, 1) 6. A (-4, 2), B (-2, 6), C (6, 6), D (8, 2 Find the area of each polygon with the given vertices. p. 617 7. S (3, 8), T (8, 3), U (2, 1) 8. L (3, 5), M (6, 8), N (9, 6), P (5, 0. 618 9. Find the area and perimeter of each polygon shown. Use your results to draw a polygon with a perimeter of 12 units ...
5, and y = x 20. y = -5, x = 2, and y = -2x + 7 21. Transportation The graph shows the speed of a boat versus time. a. If the base of each square on the graph represents 1 hour and the height represents 20 miles per hour, what is the area of one square on the graph? Include units in your answer. b. Estimate the shaded...
EXTEND Algebra Estimate the shaded area under each curve. 28. y = x 2 for 0 ≤ x ≤ 3 27. y = 2 x for 0 ≤ x ≤ 3 29. y = √  x for 0 ≤ x ≤ 9 30. Estimation Use a composite figure and the Distance Formula to estimate the perimeter of the irregular shape. 31. Graph a regular octagon on the coordinate plane with vertices on...
216 cm 2 original dimensions: A = bh = 12 (9) = 108 cm 2 Notice that 216 = 2 (108). If the height is doubled, the area is also doubled. B The base length of the triangle with vertices A(1, 1), B(6, 1), and C (3, 5) is multiplied by 1 __. 2 Draw the triangle in a coordinate plane and find the base and height. original ...
9) = 3 3 The perimeter is multiplied by 1 __ 3. The area is multiplied by ( 1 __ 3 ), or 1 __ 9. 2 1 __ (18π) = 6π 3 1 __ (81π) = 9π 9 2. The base and height of the triangle with vertices P (2, 5), Q (2, 1) and R (7, 1) are tripled. Describe the effect on its area and perimeter. When all the dimensions of a figure are ...
is multiplied by 1 __ 2, what happens to the side length? E X A M P L E 4 Entertainment Application The graph shows that DVD shipments totaled about 182 million in 2000, 364 million in 2001, and 685 million in 2002. The height of each DVD is used to represent the number of DVDs shipped. Explain why the graph is mislea...
local newspaper that is 2 inches wide p. 624 and 4 inches high and costs $36.75 per week. The cost of each ad is based on its area. If the owner of the restaurant decides to double the width and height of the ad, how much will the new ad cost? Independent Practice Describe the effect of each change on the area of the ...
by 1 _. 7 21. 21. The perimeter of an equilateral triangle is doubled. 22. 22. Find the area of the trapezoid. Describe the effect of each change on the area. a. a. The length of the top base is doubled. b. The length of both bases is doubled. c. The height is doubled. d. Both bases and the height are doubled. 23. Geo...
. The area is reduced by a factor of 1 __. 2 The area is doubled. The area is increased by a factor of 4. 31. If the area of a circle is increased by a factor of 4, what is the change in the diameter of the circle? The diameter is 1 __ of the original diameter. 2 The diameter is 2 times the original diameter. The diame...
M (5, 2), and N (1, -5) 43. A (-4, 2), M (-2, 4), C (4, 2) and D (2, -4) 9- 5 Effects of Changing Dimensions Proportionally 627 627 �� Probability Probability An experiment is an activity in which results are observed. Each result of an experiment is called an outcome. The sample space is the set o...
below are placed in a bag. An experiment consists of drawing a tile at random from the bag. A What is the sample space of the experiment? The sample space has 9 possible outcomes. The outcomes are 1, 2, 3, 4, A, B, C, D, E, and F. B What is the probability of choosing a 3 or a vowel? The event “choosing a 3” contains ...
in the event number of outcomes in the sample space. Geometric probability is used when an experiment has an infinite number of outcomes. In geometric probability, the probability of an event is based on a ratio of geometric measures such as length or area. The outcomes of an experiment may be points on a segment or i...
out of every 60 seconds. B If you arrive at the light 50 times, predict about how many times you will have to stop and wait more than 10 seconds. In the model, the event of stopping and waiting more than 10 seconds is represented by a segment that starts at C and ends 10 units from D. The probability of stopping and w...
) = 900 m 2. The probability is P = 187 _ 900 ≈ 0.21. B the trapezoid The area of the trapezoid is 3 + 12) (10) = 75 m 2. 2 The area of the rectangle is A = bh = 45 (20) = 900 m 2. The probability is P = 75 _ 900 ≈ 0.08. C the circle The area of the circle is ) = 36π ≈ 113.1 m 2. The area of the rectangle is A = bh = 4...
. the pointer not landing on red 11. the pointer landing on yellow or blue. 632 Multi-Step Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth. 12. the triangle 13. the trapezoid 14. the square 15. the part of the rectangle that does not include the sq...
90°. The angle measure of the yellow region is 135°, and the angle measure of the blue region is 135°. Which value of the probability of the spinner landing on yellow is incorrect? Explain. Algebra A point is chosen randomly inside rectangle ABCD with vertices A (2, 8), B (15, 8), C (15, 1), and D (2, 1). Find the pro...
each figure. Describe an event with a probability of 1 __. 2 39. 41. 40. 42. If a fly lands randomly on the tangram, what is the probability that it will land on each of the following pieces? a. the blue parallelogram b. the medium purple triangle c. the large yellow triangle d. Write About It Do the probabilities cha...
on the grid, what is the probability that it will be in a red region? 50. You are designing a target that is a square inside an 18 ft by 24 ft rectangle. What size should the square be in order for the target to have a probability of 1 __ 3? to have a probability of 3 __ 4? 51. Recreation How would you design a spinne...
the expressions as a ratio and simplify to determine the probability of the center of the penny landing in the shaded area. 3. Explain why the formula in the activity can be used to estimate π. 9-6 Geometry Lab 637 637 � SECTION 9B Applying Geometric Formulas Step Right Up! A booster club organizes a carnival to raise...
. N (-3, 1), P (3, 3), Q (5, 1), R (2, -4) 9-5 Effects of Changing Dimensions Proportionally Describe the effect of each change on the perimeter and area of the given figure. 5. The side length of the square is tripled. 6. The diagonals of a rhombus in which d 1 = 3 ft and d 2 = 9 ft are both multiplied by 1 __ 3. 7. T...
of a regular polygon............ 601 geometric probability................. 630 central angle of a regular polygon...... 601 Complete the sentences below with vocabulary words from the list above. 1. A(n)? is the length of a segment perpendicular to a side of a regular polygon. ̶̶̶̶ 2. The point that is equidistant fr...
2 = 18 m 640 640 Chapter 9 Extending Perimeter, Circumference, and Area �� 9-2 Developing Formulas for Circles and Regular Polygons (pp. 600–605) E X A M P L E S Find each measurement. ■ the circumference and area of ⊙B in terms of π C = 2πr = 2π (5xy) = 10xyπ m A = π r 2 = ...
cm 2 20. Study Guide: Review 641 641 �� 9-4 Perimeter and Area in the Coordinate Plane (pp. 616–621) TEKS G.7.A, G.7.B EXERCISES G.8.A Estimate the area of each irregular shape. 21. 22. Draw and classify the polygon with th...
The perimeter is 4 √  10 units. US ⋅ RT = 1 _ d 1 d 2 = 1 _ The area is A = 1 _ (2 ⋅ 6) 2 2 2 = 6 units 2. ■ Find the area of the polygon with vertices A (-3, 4), B (2, 3), C (0, -2), and D (-5, -1). area of rectangle: 7 (6) = 42 units 2 area of triangles: a: A = 1 _ (2) (5) 2 = 5 units 2 b: A = 1 _ (5) (1) 2 = 2.5 u...
A with radius 11 m is multiplied by 1 _. 2 34. The base and height of a triangle with base 8 ft and height 20 ft are both multiplied by 4. 9-6 Geometric Probability (pp. 630–636) TEKS G.8.A E X A M P L E S EXERCISES A point is chosen randomly on probability of each event. ̶̶ WZ. Find the A point is chosen randomly on p...
with diameter 12 in. Give your answers in terms of π. 5. Find the area of a regular hexagon with a side length of 14 m. Round to the nearest tenth. Find the shaded area. Round to the nearest tenth, if necessary. 6. 7. 8. The diagram shows a plan for a pond. Use a composite figure to estimate the pond’s area. The grid ...
student-produced response questions, for which you enter the correct answer in a special grid. On the SAT, the student-produced response items do not have a penalty for incorrect answers. If you are uncertain of your answer and do not have time to rework the problem, you should still grid in the answer you have. You m...
of a circle, area of a rectangle What do I substitute for each variable in the formulas? To use the formula for the area of a circle, I need to know the radius. The diameter of the circle is 5 m, so the radius is 2.5 m. I should substitute 2.5 for r and 3.14 for π. To use the formula for the area of a rectangle, I nee...
miles? 5. What formula(s) would you use to solve this problem? 6. What would you substitute for each variable in the formula? 7. After substituting the variables in the formula, what would you need to do to find the correct answer? Item D Gridded Response A point is chosen randomly inside the rectangle. What is the pr...
.5 meters 56.8 meters 61.6 meters 12 18 24 36 3. What is the length of ̶̶ VY? 1.6 2 2.5 4 4. A sailor on a ship sights the light of a lighthouse at an angle of elevation of 15°. If the light in the lighthouse is 189 feet higher than the sailor’s line of sight, what is the horizontal distance between the ship and the li...
Response 16. Two gas stations on a straight highway are 8 miles apart. If a car runs out of gas at a random point between the two gas stations, what is the probability that the car will be at least 2 miles from either gas station? Draw a diagram or write and explanation to show how you determined your answer. 17. Use ...
gruent E. a figure made up of simple shapes, such as triangles, rectangles, trapezoids, and circles Find Area in the Coordinate Plane Find the area of each figure with the given vertices. 5. △ABC with A (0, 3), B (5, 3), and C (2, -1) 6. rectangle KLMN with K (-2, 3), L (-2, 7), M (6, 7), and N (6, 3) 7. ⊙P with center...
ening a pencil. How do you think this relates to a cone? 3. What does the word surface mean? What do you think the surface area of a three-dimensional figure is? Geometry TEKS Les. 10-1 Les. 10-2 10-3 Geo. Lab Les. 10-3 Les. 10-4 10-4 Geo. Lab Les. 10-5 Les. 10-6 Les. 10-7 Les. 10-8 G.1.C Geometric structure* compare a...
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their bases. Triangular prism Rectangular prism Pentagonal prism Hexagonal prism Triangular pyramid Rectangular pyramid Pentagonal pyramid Hexagonal pyramid 654 654 Chapter 10 Spatial Reasoning �� E X A M P L E 1 Classifying Three-Dimensional Figures Classify each figure. Name...
CUSS 1. Compare prisms and cylinders. 2. GET ORGANIZED Copy and complete the graphic organizer. 656 656 Chapter 10 Spatial Reasoning �� 10-1 Exercises Exercises KEYWORD: MG7 10-1 KEYWORD: MG7 Parent GUIDED PRACTICE 1. Vocabulary A? has two circular bases. (prism, cyli...
the Multi-Step TAKS Prep on page 678. A manufacturer of camping gear makes a wall tent in the shape shown in the diagram. a. Classify the three-dimensional figure that the wall tent forms. b. What shapes make up the faces of the tent? How many of each shape are there? c. Draw a net for the wall tent. 658 658 Chapter 1...
have? � � � � � � � � SPIRAL REVIEW Write the equation that fits the description. (Previous course) 52. the equation of the graph that is the reflection of the graph of y = x 2 over the x-axis 53. the equation of the graph of y = x 2 after a vertical translation of 6 units upward 54. the quadratic equation of a graph ...
hidden cubes. 2. Draw an isometric view of the given object. Assume there are no hidden cubes. In a perspective drawing, nonvertical parallel lines are drawn so that they meet at a point called a vanishing point. Vanishing points are located on a horizontal line called the horizon. A one-point perspective drawing cont...
given object. Assume there are no hidden cubes. B D A C Yes; the drawing is a one-point perspective view of the object. No; the cubes that share a face in the object do not share a face in the drawing. No; the figure in the drawing is made up of four cubes, and the object is made up of only three cubes. Yes; the drawi...
KS TEKS TAKS TAKS Skills Practice p. S22 Application Practice p. S37 Draw each object in one-point and two-point perspective. Assume there are no hidden cubes. 20. right triangular prism 21. block letter Determine whether each drawing represents the given object. Assume there are no hidden cubes. 22. 23. 24. 25. 26. Us...
the entire cone. b. Draw all six orthographic views of the frustum. c. Draw a net for the frustum. 42. Art Draw a one-point or two-point perspective drawing of the inside of a room. Include at least two pieces of furniture drawn in perspective. SPIRAL REVIEW Find the two numbers. (Previous course) 43. The sum of two n...
.9.D Use geometry software or a compass and straightedge to create a larger version of each net on heavy paper. Fold each net into a polyhedron. NAME FACES EXAMPLE NET REGULAR POLYHEDRONS Tetrahedron 4 triangles Octahedron 8 triangles Icosahedron 20 triangles Cube 6 squares Dodecahedron 12 pentagons Try This 1. Complet...
Simplify. 10 - 15 + 7 ≟ 2 2 = 2 Find the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler’s formula. 1a. 1b. 670 670 Chapter 10 Spatial Reasoning A diagonal of a three-dimensional figure connects two vertices of two different faces. Diagonal d of a rectangular prism is shown in ...
the z-axis. An ordered triple (x, y, z) is used to locate a point. To locate the point (3, 2, 4), start at (0, 0, 0). From there move 3 units forward, 2 units right, and then 4 units up. E X A M P L E 3 Graphing Figures in Three Dimensions Graph each figure. A a cube with edge length 4 units and one vertex at (0, 0, 0...
�� (. The midpoint of the segment with endpoints ( x 1, y 1, z 1 ) and ( x 2, y 2, z 2 ) is Finding Distances and Midpoints in Three Dimensions Find the distance between the given points. Find the midpoint of the segment with the given endpoints. Round to the nearest tenth, if necessary. A (0, 0, 0) and (3...
�� 16 + 16 + 25 = √  57 ≈ 7.5 units Find the distance between the given points. Find the midpoint of the segment with the given endpoints. Round to the nearest tenth, if necessary. 4a. (0, 9, 5) and (6, 0, 12) 4b. (5, 8, 16) and (12, 16, 20) E X A M P L E 5 Recreation Application Two divers swam from a boat to the loc...
MG7 Parent GUIDED PRACTICE 1. Vocabulary Explain why a cylinder is not a polyhedron. 670 Find the number of vertices, edges, and faces of each polyhedron. Use your results to verify Euler’s formula. 2. 3. 4 Find the unknown dimension in each figure. Round to the nearest tenth, if necessary. p. 671 5. the length of the...
a 15 m by 6 m base and a 17 m diagonal 20. the edge length of a cube with an 8 cm diagonal 674 674 Chapter 10 Spatial Reasoning Meteorology A typical cumulus cloud weighs about 1.4 billion pounds, which is more than 100,000 elephants. Source: usgs.gov Graph each figure. 21. a cylinder with radius 5 units, height 3 uni...
S Prep on page 678. ̶̶̶ NM ≅ ̶̶ NP The tent at right is a triangular prism where ̶̶ KJ ≅ ̶̶ KL and has the given dimensions. and a. The tent manufacturer sets up the tent on a coordinate system so that J is at the origin and M has coordinates (7, 0, 0). Find the coordinates of the other vertices. b. The manufacturer wa...
(2, 2, 6) 50. (2, 8, 5) and (3, 6, 3) 51. Multi-Step Find z if the distance between R (6, -1, -3) and S (3, 3, z) is 13. 52. Draw a figure with 6 vertices and 6 faces. 53. Estimation Measure the net for a rectangular prism and estimate the length of a diagonal. 54. Make a Conjecture What do you think is the longest se...
(-1, 2, 4), B (1, -2, 6), and C (3, -6, 8) are collinear. 62. Algebra Write a coordinate proof of the Midpoint Formula using the Distance Formula. Given: points ), and M ( Prove: A, B, and M are collinear, and AM = MB _____ _____ _____ 2, 2, 2 63. Algebra Write a coordinate proof that the diagonals of a rectangular pr...
shape of the tent. Draw the catalog display for each tent. The manufacturer uses a three-dimensional coordinate system to represent the vertices of each tent. Each unit of the coordinate system represents one foot. 2. Which tent offers a greater sleeping area? 3. Compare the heights of the tents. Which tent offers mor...
the midpoint of the segment with the given endpoints. Round to the nearest tenth, if necessary. 19. (3, 1, -2) and (5, -5, 7) 18. (0, 0, 0) and (4, 6, 12) 20. (3, 5, 9) and (7, 2, 0) Ready to Go On? 679 679 �� 10-4 Surface Area of Prisms and Cylinders TEKS G.8.D Congruence and the geometry of size: find...
of a right rectangular prism with length ℓ, width w, and height h can be written as S = 2ℓw + 2wh + 2ℓh. 680 680 Chapter 10 Spatial Reasoning �� E X A M P L E 1 Finding Lateral Areas and Surface Areas of Prisms Find the later...
(1) (5) = 10π m 2 S = L + 2π r 2 = 10π + 2π (1) 2 = 12π m 2 The radius is half the diameter, or 1 m. B a cylinder with a circumference of 10π cm and a height equal to 3 times the radius Step 1 Use the circumference to find the radius. C = 2πr 10π = 2πr r = 5 Circumference of a circle Substitute 10π for C. Divide both ...
original dimensions: length, width, and height doubled: S = Ph + 2B = 16 (3) + 2 (6) (2) = 72 in 2 S = Ph + 2B = 32 (6) + 2 (12) (4) = 288 in 2 Notice that 288 = 4 (72). If the length, width, and height are doubled, the surface area is multiplied by 2 2, or 4. 4. The height and diameter of the cylinder are multiplied ...
prism have Find the lateral area and surface area of each right prism. p. 681 2. 3. 4. a cube with edge length 9 inches. 682 Find the lateral area and surface area of each right cylinder. Give your answers in terms of π. 5. 6. 7. a cylinder with base area 64π m 2 and a height 3 meters less than the radius. 682 Multi-S...
ylinders 685 685 �� 24. Find the height of a right cylinder with surface area 160π ft 2 and radius 5 ft. 25. Find the height of a right rectangular prism with surface a...
. Round to the nearest tenth. 686 686 Chapter 10 Spatial Reasoning 10 ftge07sec10l04004aa1st pass4/23/5cmurphy10 ft10 ftge07sec10l04005a1st pass4/12/5cmurphy10 ft10 ft�� 38. Measure the dimensions of the net of a cylinder to the nearest millimeter. Which is closest to the surface area of the ...
right views of each object. Assume there are no hidden cubes. (Lesson 10-2) 48. 49. 50. 10- 4 Surface Area of Prisms and Cylinders 687 687 �� 10-4 Model Right and Oblique Cylinders In Lesson 10-4, you learned the difference between right and oblique cylinders. In this lab, you will make mode...
altitude of a pyramid vertex of a cone axis of a cone right cone oblique cone slant height of a right cone altitude of a cone Also G.5.A, G.5.B, G.6.B, G.11.D Why learn this? A speaker uses part of the lateral surface of a cone to produce sound. Speaker cones are usually made of paper, plastic, or metal. (See Example ...
__ 2 (2 √  3 ) (24) = 24 √  3 m 2. Step 2 Find the lateral area. Pℓ L = 1 _ 2 = 1 _ (24) (7) = 84 m 2 2 Step 3 Find the surface area. S = 1 _ 2 Pℓ + B Lateral area of a regular pyramid Substitute 24 for P and 7 for ℓ. Surface area of a regular pyramid = 84 + 24 √  3 ≈ 125.6 cm 2 Substitute 24 √  3 for B. 1. Find t...
agorean Theorem to find ℓ. ℓ = √  5 2 + 12 2 = 13 ft Step 2 Find the lateral area and surface area. L = πrℓ = π (5) (13) = 65π ft 2 S = πrℓ + π r 2 = 65π + π (5) 2 = 90π ft 2 Lateral area of a right cone Substitute 5 for r and 13 for ℓ. Surface area of a right cone Substitute 5 for r and 13 for ℓ. 2. Find the later...
(cone lateral area) + (cylinder lateral area) + (base area) = 2520π + 784π + 1484π = 4788π cm 2 4. Find the surface area of the composite figure. E X A M P L E 5 Electronics Application Electronics The paper cones of The paper cones of antique speakers were both functional and decorative. Some had elaborate patterns o...
effect of each change on the surface area of the given figure. p. 691 8. The dimensions are cut in half. 9. The dimensions are tripled Find the surface area of each composite figure. p. 692 10. 11. 692 12. Crafts Anna is making a birthday hat from a pattern that is 3 __ 4 of a circle of colored paper. If Anna’s head i...
is a regular square pyramid with the dimensions shown. a. Find the surface area of the container to the nearest tenth. b. The manufacturer decides to make a container in the shape of a right cone that requires the same amount of material. The base diameter must be 9 cm. Find the slant height of the container to the ne...

the pattern below. 1, 3, 7, 13, 21, … 15. In △XYZ, ∠X and ∠Z are remote interior angles of exterior ∠XYT. If m∠X = (x + 15) °, m∠Z = (50 - 3x) °, and m∠XYT = (4x - 25) °, what is the value of x? 16. In △ABC and △DEF, ∠A ≅ ∠F. If EF = 4.5, DF = 3, ̶̶ AB would let you and AC = 1.5, what length for conclude that △ABC ∼ △...

–8 581 581 �� T E X A S TAKS Grades 9–11 Obj. 10 �� Reunion Tower The 55-story Reunion Tower is one of the most recognized buildings in the Dallas skyline. Built as a part of the Hyatt Regency Hotel, the tower is topped by a geodesic dome that houses a revolving ...

Choose one or more strategies to solve each problem. 1. In 1973, the National Park Service finished restoring President Johnson’s house to its appearance during Johnson’s childhood. The blueprint below shows the layout of the house after the restoration. Suppose there is a border of wallpaper along the edge of the cei...

m 7. 6 in. = ft 8. 15 m = mm Metric 1 kilometer = 1000 meters 1 meter = 100 centimeters 1 centimeter = 10 millimeters Customary 1 mile = 1760 yards 1 mile = 5280 feet 1 yard = 3 feet 1 foot = 12 inches Pythagorean Theorem Find x in each right triangle. Round to the nearest tenth, if necessary. 9. 11. 10. Measure with ...

2 Geo. Lab Les. 9-2 Les. 9-3 9-3 Geo. Lab Les. 9-4 Les. 9-5 Les. 9-6 9-6 Geo. Lab G.5.A Geometric patterns* use... geometric patterns to develop ★ ★ ★ algebraic expressions representing geometric properties G.5.B Geometric patterns* use... geometric patterns to make generalizations about geometric properties, including...

have already studied, and make flash cards of the formulas or theorems from the lesson. 2. Review your flash cards by looking at the front of each card and trying to recall the information on the back of the card. Extending Perimeter, Circumference, and Area 587 587 �� Literal Equations Algebra A literal equ...

a in terms of b and c, and use it to complete the following table. a b 48 36 14 c 35 36 50 588 588 Chapter 9 Extending Perimeter, Circumference, and Area �� 9-1 Developing Formulas for Triangles and Quadrilaterals TEKS G.5.A Geometric patterns: use... geometric patterns to develop algebraic expressions represent...

which b = 5 cm and A = (5 x 2 - 5x) cm 2 A = bh 5 x 2 - 5x = 5h 5 ( x 2 - x) = 5h x 2 - x = h Area of a rectangle Substitute 5 x 2 - 5x for A and 5 for b. Factor 5 out of the expression for A. Divide both sides by 5. h = ( x 2 - x) cm Sym. Prop. of = C the perimeter of the rectangle, in which A = 12 x ft 2 Step 1 Use ...

measurement. B the base of the triangle, in which A = x 2 in 2 bx bh 2x = b b = 2x in. Area of a triangle Substitute x 2 for A and x for h. Divide both sides by x. Multiply both sides by 2. Sym. Prop. of = C Area of a trapezoid b 2 of the trapezoid, in which A = 8 ft 3 + b 2 ) (2 ft Sym. Prop. of = Substitute 8 for A,...

x = 40 9 2 + y 2 = 15 2 y 2 = 144 y = 12 Step 2 Use d 1 and d 2 to find the area. d 1 is equal to x + y, which is 52. Half of d 2 is equal to 9, so d 2 is equal to 1852) (18) 2 A = 468 ft 2 Substitute 52 for d 1 and 18 for d 2. Area of a kite Simplify. 3. Find d 2 of a rhombus in which d 1 = 3x m and A = 12xy Games Ap...

triangle, in which p. 590 A = 58.5 in 2 6. b 1 of a trapezoid in which A = (48x + 68) in 2, h = 8 in., and b 2 = (9x + 12) in. the area of the rhombus p. 591 8. d 2 of the kite, in which A = 187.5 m 2 9. d 2 of a kite in which A = 12 x 2 y 3 cm 2, d 1 = 3xy cm 10. Art The stained-glass window shown is a rectangle p. 5...

�AEJ 22. trapezoid ABFJ � � � � � � � � � Multi-Step Find the area of each figure. Round to the nearest tenth, if necessary. 23. 24. 25. Write each area in terms of x. 26. equilateral triangle 27. 30°-60°-90° triangle 28. 45°-45°-90° triangle 594 594 Chapter 9 Extending Perimeter, Circumference, and Area ��...

12 in. President James Garfield was a classics professor and a major general in the Union Army. He was assassinated in 1881. Source: www.whitehouse.gov 43. The following proof of the Pythagorean Theorem was discovered by President James Garfield in 1876 while he was a member of the House of Representatives. a. Write t...

51. Write About It A square is also a parallelogram, a rectangle, and a rhombus. Prove that the area formula for each shape gives the same result as the formula for the area of a square. 52. Which expression best represents the area of the rectangle? 2x + 2 (x - c) x (x - c) x 2 + (x - c) 2 2x (x - c) 53. The length o...

lengths of the rectangle. Solve the perimeter formula 2x + 2y = 24 for y, and substitute the expression into the area formula A = xy. b. Graph the resulting function on a coordinate plane. What are the domain and range of the function? c. What are the dimensions of the rectangle that will enclose the greatest area? d....

possible. How could you use this π measuring tape to find the diameter of a circular object? Use your π measuring tape to measure 5 circular objects. Give the circumference and diameter of each object. 598 598 Chapter 9 Extending Perimeter, Circumference, and Area Archimedes used inscribed and circumscribed polygons t...

of a regular polygon apothem central angle of a regular polygon Who uses this? Drummers use drums of different sizes to produce different notes. The pitch is related to the area of the top of the drum. (See Example 2.) A circle is the locus of points in a plane that are a fixed distance from a point called the center ...

the circumference. C = 2πr C = 2π (3x) Substitute 3x for r. C = 6xπ cm Simplify. 1. Find the area of ⊙A in terms of π in which C = (4x - 6) π m. E X A M P L E 2 Music Application A drum kit contains three drums with diameters of 10 in., 12 in., and 14 in. Find the area of the top of each drum. Round to the nearest ten...

° Triangle Theorem, the apothem is 3 √  3 m3 √  3 ) (36) 2 aP Area of a regular polygon Substitute 3 √  3 for a and 36 for P. The tangent of an angle in a right triangle is the ratio of the opposite leg length to the adjacent leg length. See page 525. A = 54 √  3 ≅ 93.5 m 2 Simplify. B a regular pentagon with side ...

pizzas with diameters of 8 in., 10 in., and 12 in. p. 601 Find the area of each size pizza. Round to the nearest tenth Find the area of each regular polygon. Round to the nearest tenth. p. 602 6. 7. Independent Practice For See Exercises Example 10–12 13 14–17 1 2 3 TEKS TEKS TAKS TAKS Skills Practice p. S20 Applicati...

circumference of 2π in. Which calculation of the area is incorrect? Explain. Find the missing measurements for each circle. Give your answers in terms of π. Diameter d Radius r Area A Circumference C 6 34. 35. 36. 37. 100 17 36 π 38. Multi-Step Janet is designing a garden around a gazebo that is a regular hexagon with...

the table top that includes a 2-foot-by-1-foot rectangle and 4 squares with sides 0.5 foot long. Which information makes this scenario impossible? There will be no room left on the tabletop after the rectangle has been painted. A 2-foot-long rectangle will not fit on the circular tabletop. Squares cannot be painted on...

necessary. A B Divide the figure into rectangles. Divide the figure into parts. The base of the triangle is √  10. 2 2 - 4. 8 2 = 9 ft. area of top rectangle: A = bh = 12 (15) = 180 c m 2 area of bottom rectangle: A = bh = 9 (27) = 243 c m 2 shaded area: 180 + 243 = 423 c m 2 area of triangle: A = 1 __ 2 bh = 1 _...

A newly planted xeriscape uses 17 gallons of water per square foot per year. How much water will the garden require in one year? To find the area of the garden in square feet, divide the garden into parts. The area of the top rectangle is 28.5 (7.5) = 213.75 f t 2. The area of the center trapezoid is 1 __ 2 (12 + 18) ...

+ 3 + 2.5 + 1 = 8 cm 2 The shaded area is about 8 c m 2. 4. Use a composite figure to estimate the shaded area. The grid has squares with side lengths of 1 ft. THINK AND DISCUSS 1. Describe a composite figure whose area you could find by using subtraction. 2. Explain how to find the area of an irregular shape by using...

Give your answers in terms of π. 18. 19. 20. 21. Geography Use the grid on the map of Lake Superior to estimate the area of the surface of the lake. Each square on the grid has a side length of 100 miles. 22. Critical Thinking A trapezoid can be divided into a rectangle and two triangles. Show that the area formula fo...

each irregular shape and draw a composite figure that approximates it. Measure the composite figure and use it to estimate the area of the irregular shape. 28. 29. 30. Write About It Explain when you would use addition to find the area of a composite figure and when you would use subtraction. 31. Which equation can be...

What technical materials do you write? A: I write training manuals for computer software packages. Q: How do you use math? A: Some manuals I write are for math programs, so I use a lot of formulas to describe patterns and measurements. Q: What are your future plans? A: After I get a few more years experience writing m...

signs are usually made of reflective aluminum. A manufacturer of traffic signs begins with a rectangular sheet of aluminum that measures 60 in. by 90 in. 1. A railroad crossing sign is a circle with a diameter of 30 in. The manufacturer can make 6 of these signs from the sheet of aluminum by arranging the signs as sho...

15 �� 9-4 Perimeter and Area in the Coordinate Plane TEKS G.7.A Dimensionality and the geometry of location: use... two-dimensional coordinate systems to represent... figures. Also G.7.B, G.8.A Objective Find the perimeters and are...

m = See pages 44 and 182. Step 1 Draw the polygon. slope of Step 2 ABCD appears to be a rectangle. To verify this, use slopes to show that the sides are perpendicular. ̶̶ = 3 _ AB : - (-4) ̶̶ BC : 0 - 4 _ = -4 _ 4 - 2 2 ̶̶ = -3 _ CD : -3 - 0 _ = 1 _ -6 -2 - 4 2 1- (-3) = 4 _ _ -2 -4 - (-2) slope of slope of slope of ̶...

, -3), and Z (-4, 0). Draw the polygon and enclose it in a rectangle. area of the rectangle: A = bh = 8 (7) = 56 units 2 area of the triangles: bh = 1 _ a: A = 1 _ (5) (4) = 10 units 2 2 2 bh = 1 _ b: A = 1 _ (3) (2) = 3 units 2 2 2 bh = 1 _ c: A = 1 _ (2) (5) = 5 units 2 2 2 bh = 1 _ d: A = 1 _ (6) (3) = 9 units 2 2 2...

its 2 2 2 blue triangle: bh = 1 _ A = 1 _ (3) (1) = 1.5 u nits 2 2 2 green rectangle: A = bh = (3) (1) = 3 units 2 yellow rectangle: A = bh = (2) (1) = 2 units 2 yellow rectangle: A = bh = (2) (1) = 2 units 2 The areas are the same. Both figures have an area of 5 + 1.5 + 3 + 2 = 11.5 units 2. If the figures were triang...

(8, 1), S (-2, 1) 6. A (-4, 2), B (-2, 6), C (6, 6), D (8, 2 Find the area of each polygon with the given vertices. p. 617 7. S (3, 8), T (8, 3), U (2, 1) 8. L (3, 5), M (6, 8), N (9, 6), P (5, 0. 618 9. Find the area and perimeter of each polygon shown. Use your results to draw a polygon with a perimeter of 12 units ...

5, and y = x 20. y = -5, x = 2, and y = -2x + 7 21. Transportation The graph shows the speed of a boat versus time. a. If the base of each square on the graph represents 1 hour and the height represents 20 miles per hour, what is the area of one square on the graph? Include units in your answer. b. Estimate the shaded...

EXTEND Algebra Estimate the shaded area under each curve. 28. y = x 2 for 0 ≤ x ≤ 3 27. y = 2 x for 0 ≤ x ≤ 3 29. y = √  x for 0 ≤ x ≤ 9 30. Estimation Use a composite figure and the Distance Formula to estimate the perimeter of the irregular shape. 31. Graph a regular octagon on the coordinate plane with vertices on...

216 cm 2 original dimensions: A = bh = 12 (9) = 108 cm 2 Notice that 216 = 2 (108). If the height is doubled, the area is also doubled. B The base length of the triangle with vertices A(1, 1), B(6, 1), and C (3, 5) is multiplied by 1 __. 2 Draw the triangle in a coordinate plane and find the base and height. original ...

9) = 3 3 The perimeter is multiplied by 1 __ 3. The area is multiplied by ( 1 __ 3 ), or 1 __ 9. 2 1 __ (18π) = 6π 3 1 __ (81π) = 9π 9 2. The base and height of the triangle with vertices P (2, 5), Q (2, 1) and R (7, 1) are tripled. Describe the effect on its area and perimeter. When all the dimensions of a figure are ...

is multiplied by 1 __ 2, what happens to the side length? E X A M P L E 4 Entertainment Application The graph shows that DVD shipments totaled about 182 million in 2000, 364 million in 2001, and 685 million in 2002. The height of each DVD is used to represent the number of DVDs shipped. Explain why the graph is mislea...

local newspaper that is 2 inches wide p. 624 and 4 inches high and costs $36.75 per week. The cost of each ad is based on its area. If the owner of the restaurant decides to double the width and height of the ad, how much will the new ad cost? Independent Practice Describe the effect of each change on the area of the ...

by 1 _. 7 21. 21. The perimeter of an equilateral triangle is doubled. 22. 22. Find the area of the trapezoid. Describe the effect of each change on the area. a. a. The length of the top base is doubled. b. The length of both bases is doubled. c. The height is doubled. d. Both bases and the height are doubled. 23. Geo...

. The area is reduced by a factor of 1 __. 2 The area is doubled. The area is increased by a factor of 4. 31. If the area of a circle is increased by a factor of 4, what is the change in the diameter of the circle? The diameter is 1 __ of the original diameter. 2 The diameter is 2 times the original diameter. The diame...

M (5, 2), and N (1, -5) 43. A (-4, 2), M (-2, 4), C (4, 2) and D (2, -4) 9- 5 Effects of Changing Dimensions Proportionally 627 627 �� Probability Probability An experiment is an activity in which results are observed. Each result of an experiment is called an outcome. The sample space is the set o...

below are placed in a bag. An experiment consists of drawing a tile at random from the bag. A What is the sample space of the experiment? The sample space has 9 possible outcomes. The outcomes are 1, 2, 3, 4, A, B, C, D, E, and F. B What is the probability of choosing a 3 or a vowel? The event “choosing a 3” contains ...

in the event number of outcomes in the sample space. Geometric probability is used when an experiment has an infinite number of outcomes. In geometric probability, the probability of an event is based on a ratio of geometric measures such as length or area. The outcomes of an experiment may be points on a segment or i...

out of every 60 seconds. B If you arrive at the light 50 times, predict about how many times you will have to stop and wait more than 10 seconds. In the model, the event of stopping and waiting more than 10 seconds is represented by a segment that starts at C and ends 10 units from D. The probability of stopping and w...

) = 900 m 2. The probability is P = 187 _ 900 ≈ 0.21. B the trapezoid The area of the trapezoid is 3 + 12) (10) = 75 m 2. 2 The area of the rectangle is A = bh = 45 (20) = 900 m 2. The probability is P = 75 _ 900 ≈ 0.08. C the circle The area of the circle is ) = 36π ≈ 113.1 m 2. The area of the rectangle is A = bh = 4...

. the pointer not landing on red 11. the pointer landing on yellow or blue. 632 Multi-Step Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth. 12. the triangle 13. the trapezoid 14. the square 15. the part of the rectangle that does not include the sq...

90°. The angle measure of the yellow region is 135°, and the angle measure of the blue region is 135°. Which value of the probability of the spinner landing on yellow is incorrect? Explain. Algebra A point is chosen randomly inside rectangle ABCD with vertices A (2, 8), B (15, 8), C (15, 1), and D (2, 1). Find the pro...

each figure. Describe an event with a probability of 1 __. 2 39. 41. 40. 42. If a fly lands randomly on the tangram, what is the probability that it will land on each of the following pieces? a. the blue parallelogram b. the medium purple triangle c. the large yellow triangle d. Write About It Do the probabilities cha...

on the grid, what is the probability that it will be in a red region? 50. You are designing a target that is a square inside an 18 ft by 24 ft rectangle. What size should the square be in order for the target to have a probability of 1 __ 3? to have a probability of 3 __ 4? 51. Recreation How would you design a spinne...

the expressions as a ratio and simplify to determine the probability of the center of the penny landing in the shaded area. 3. Explain why the formula in the activity can be used to estimate π. 9-6 Geometry Lab 637 637 � SECTION 9B Applying Geometric Formulas Step Right Up! A booster club organizes a carnival to raise...

. N (-3, 1), P (3, 3), Q (5, 1), R (2, -4) 9-5 Effects of Changing Dimensions Proportionally Describe the effect of each change on the perimeter and area of the given figure. 5. The side length of the square is tripled. 6. The diagonals of a rhombus in which d 1 = 3 ft and d 2 = 9 ft are both multiplied by 1 __ 3. 7. T...

of a regular polygon............ 601 geometric probability................. 630 central angle of a regular polygon...... 601 Complete the sentences below with vocabulary words from the list above. 1. A(n)? is the length of a segment perpendicular to a side of a regular polygon. ̶̶̶̶ 2. The point that is equidistant fr...

2 = 18 m 640 640 Chapter 9 Extending Perimeter, Circumference, and Area �� 9-2 Developing Formulas for Circles and Regular Polygons (pp. 600–605) E X A M P L E S Find each measurement. ■ the circumference and area of ⊙B in terms of π C = 2πr = 2π (5xy) = 10xyπ m A = π r 2 = ...

cm 2 20. Study Guide: Review 641 641 �� 9-4 Perimeter and Area in the Coordinate Plane (pp. 616–621) TEKS G.7.A, G.7.B EXERCISES G.8.A Estimate the area of each irregular shape. 21. 22. Draw and classify the polygon with th...

The perimeter is 4 √  10 units. US ⋅ RT = 1 _ d 1 d 2 = 1 _ The area is A = 1 _ (2 ⋅ 6) 2 2 2 = 6 units 2. ■ Find the area of the polygon with vertices A (-3, 4), B (2, 3), C (0, -2), and D (-5, -1). area of rectangle: 7 (6) = 42 units 2 area of triangles: a: A = 1 _ (2) (5) 2 = 5 units 2 b: A = 1 _ (5) (1) 2 = 2.5 u...

A with radius 11 m is multiplied by 1 _. 2 34. The base and height of a triangle with base 8 ft and height 20 ft are both multiplied by 4. 9-6 Geometric Probability (pp. 630–636) TEKS G.8.A E X A M P L E S EXERCISES A point is chosen randomly on probability of each event. ̶̶ WZ. Find the A point is chosen randomly on p...

with diameter 12 in. Give your answers in terms of π. 5. Find the area of a regular hexagon with a side length of 14 m. Round to the nearest tenth. Find the shaded area. Round to the nearest tenth, if necessary. 6. 7. 8. The diagram shows a plan for a pond. Use a composite figure to estimate the pond’s area. The grid ...

student-produced response questions, for which you enter the correct answer in a special grid. On the SAT, the student-produced response items do not have a penalty for incorrect answers. If you are uncertain of your answer and do not have time to rework the problem, you should still grid in the answer you have. You m...

of a circle, area of a rectangle What do I substitute for each variable in the formulas? To use the formula for the area of a circle, I need to know the radius. The diameter of the circle is 5 m, so the radius is 2.5 m. I should substitute 2.5 for r and 3.14 for π. To use the formula for the area of a rectangle, I nee...

miles? 5. What formula(s) would you use to solve this problem? 6. What would you substitute for each variable in the formula? 7. After substituting the variables in the formula, what would you need to do to find the correct answer? Item D Gridded Response A point is chosen randomly inside the rectangle. What is the pr...

.5 meters 56.8 meters 61.6 meters 12 18 24 36 3. What is the length of ̶̶ VY? 1.6 2 2.5 4 4. A sailor on a ship sights the light of a lighthouse at an angle of elevation of 15°. If the light in the lighthouse is 189 feet higher than the sailor’s line of sight, what is the horizontal distance between the ship and the li...

Response 16. Two gas stations on a straight highway are 8 miles apart. If a car runs out of gas at a random point between the two gas stations, what is the probability that the car will be at least 2 miles from either gas station? Draw a diagram or write and explanation to show how you determined your answer. 17. Use ...

gruent E. a figure made up of simple shapes, such as triangles, rectangles, trapezoids, and circles Find Area in the Coordinate Plane Find the area of each figure with the given vertices. 5. △ABC with A (0, 3), B (5, 3), and C (2, -1) 6. rectangle KLMN with K (-2, 3), L (-2, 7), M (6, 7), and N (6, 3) 7. ⊙P with center...

ening a pencil. How do you think this relates to a cone? 3. What does the word surface mean? What do you think the surface area of a three-dimensional figure is? Geometry TEKS Les. 10-1 Les. 10-2 10-3 Geo. Lab Les. 10-3 Les. 10-4 10-4 Geo. Lab Les. 10-5 Les. 10-6 Les. 10-7 Les. 10-8 G.1.C Geometric structure* compare a...

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their bases. Triangular prism Rectangular prism Pentagonal prism Hexagonal prism Triangular pyramid Rectangular pyramid Pentagonal pyramid Hexagonal pyramid 654 654 Chapter 10 Spatial Reasoning �� E X A M P L E 1 Classifying Three-Dimensional Figures Classify each figure. Name...

CUSS 1. Compare prisms and cylinders. 2. GET ORGANIZED Copy and complete the graphic organizer. 656 656 Chapter 10 Spatial Reasoning �� 10-1 Exercises Exercises KEYWORD: MG7 10-1 KEYWORD: MG7 Parent GUIDED PRACTICE 1. Vocabulary A? has two circular bases. (prism, cyli...

the Multi-Step TAKS Prep on page 678. A manufacturer of camping gear makes a wall tent in the shape shown in the diagram. a. Classify the three-dimensional figure that the wall tent forms. b. What shapes make up the faces of the tent? How many of each shape are there? c. Draw a net for the wall tent. 658 658 Chapter 1...

have? � � � � � � � � SPIRAL REVIEW Write the equation that fits the description. (Previous course) 52. the equation of the graph that is the reflection of the graph of y = x 2 over the x-axis 53. the equation of the graph of y = x 2 after a vertical translation of 6 units upward 54. the quadratic equation of a graph ...

hidden cubes. 2. Draw an isometric view of the given object. Assume there are no hidden cubes. In a perspective drawing, nonvertical parallel lines are drawn so that they meet at a point called a vanishing point. Vanishing points are located on a horizontal line called the horizon. A one-point perspective drawing cont...

given object. Assume there are no hidden cubes. B D A C Yes; the drawing is a one-point perspective view of the object. No; the cubes that share a face in the object do not share a face in the drawing. No; the figure in the drawing is made up of four cubes, and the object is made up of only three cubes. Yes; the drawi...

KS TEKS TAKS TAKS Skills Practice p. S22 Application Practice p. S37 Draw each object in one-point and two-point perspective. Assume there are no hidden cubes. 20. right triangular prism 21. block letter Determine whether each drawing represents the given object. Assume there are no hidden cubes. 22. 23. 24. 25. 26. Us...

the entire cone. b. Draw all six orthographic views of the frustum. c. Draw a net for the frustum. 42. Art Draw a one-point or two-point perspective drawing of the inside of a room. Include at least two pieces of furniture drawn in perspective. SPIRAL REVIEW Find the two numbers. (Previous course) 43. The sum of two n...

.9.D Use geometry software or a compass and straightedge to create a larger version of each net on heavy paper. Fold each net into a polyhedron. NAME FACES EXAMPLE NET REGULAR POLYHEDRONS Tetrahedron 4 triangles Octahedron 8 triangles Icosahedron 20 triangles Cube 6 squares Dodecahedron 12 pentagons Try This 1. Complet...

Simplify. 10 - 15 + 7 ≟ 2 2 = 2 Find the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler’s formula. 1a. 1b. 670 670 Chapter 10 Spatial Reasoning A diagonal of a three-dimensional figure connects two vertices of two different faces. Diagonal d of a rectangular prism is shown in ...

the z-axis. An ordered triple (x, y, z) is used to locate a point. To locate the point (3, 2, 4), start at (0, 0, 0). From there move 3 units forward, 2 units right, and then 4 units up. E X A M P L E 3 Graphing Figures in Three Dimensions Graph each figure. A a cube with edge length 4 units and one vertex at (0, 0, 0...

�� (. The midpoint of the segment with endpoints ( x 1, y 1, z 1 ) and ( x 2, y 2, z 2 ) is Finding Distances and Midpoints in Three Dimensions Find the distance between the given points. Find the midpoint of the segment with the given endpoints. Round to the nearest tenth, if necessary. A (0, 0, 0) and (3...

�� 16 + 16 + 25 = √  57 ≈ 7.5 units Find the distance between the given points. Find the midpoint of the segment with the given endpoints. Round to the nearest tenth, if necessary. 4a. (0, 9, 5) and (6, 0, 12) 4b. (5, 8, 16) and (12, 16, 20) E X A M P L E 5 Recreation Application Two divers swam from a boat to the loc...

MG7 Parent GUIDED PRACTICE 1. Vocabulary Explain why a cylinder is not a polyhedron. 670 Find the number of vertices, edges, and faces of each polyhedron. Use your results to verify Euler’s formula. 2. 3. 4 Find the unknown dimension in each figure. Round to the nearest tenth, if necessary. p. 671 5. the length of the...

a 15 m by 6 m base and a 17 m diagonal 20. the edge length of a cube with an 8 cm diagonal 674 674 Chapter 10 Spatial Reasoning Meteorology A typical cumulus cloud weighs about 1.4 billion pounds, which is more than 100,000 elephants. Source: usgs.gov Graph each figure. 21. a cylinder with radius 5 units, height 3 uni...

S Prep on page 678. ̶̶̶ NM ≅ ̶̶ NP The tent at right is a triangular prism where ̶̶ KJ ≅ ̶̶ KL and has the given dimensions. and a. The tent manufacturer sets up the tent on a coordinate system so that J is at the origin and M has coordinates (7, 0, 0). Find the coordinates of the other vertices. b. The manufacturer wa...

(2, 2, 6) 50. (2, 8, 5) and (3, 6, 3) 51. Multi-Step Find z if the distance between R (6, -1, -3) and S (3, 3, z) is 13. 52. Draw a figure with 6 vertices and 6 faces. 53. Estimation Measure the net for a rectangular prism and estimate the length of a diagonal. 54. Make a Conjecture What do you think is the longest se...

(-1, 2, 4), B (1, -2, 6), and C (3, -6, 8) are collinear. 62. Algebra Write a coordinate proof of the Midpoint Formula using the Distance Formula. Given: points ), and M ( Prove: A, B, and M are collinear, and AM = MB _____ _____ _____ 2, 2, 2 63. Algebra Write a coordinate proof that the diagonals of a rectangular pr...

shape of the tent. Draw the catalog display for each tent. The manufacturer uses a three-dimensional coordinate system to represent the vertices of each tent. Each unit of the coordinate system represents one foot. 2. Which tent offers a greater sleeping area? 3. Compare the heights of the tents. Which tent offers mor...

the midpoint of the segment with the given endpoints. Round to the nearest tenth, if necessary. 19. (3, 1, -2) and (5, -5, 7) 18. (0, 0, 0) and (4, 6, 12) 20. (3, 5, 9) and (7, 2, 0) Ready to Go On? 679 679 �� 10-4 Surface Area of Prisms and Cylinders TEKS G.8.D Congruence and the geometry of size: find...

of a right rectangular prism with length ℓ, width w, and height h can be written as S = 2ℓw + 2wh + 2ℓh. 680 680 Chapter 10 Spatial Reasoning �� E X A M P L E 1 Finding Lateral Areas and Surface Areas of Prisms Find the later...

(1) (5) = 10π m 2 S = L + 2π r 2 = 10π + 2π (1) 2 = 12π m 2 The radius is half the diameter, or 1 m. B a cylinder with a circumference of 10π cm and a height equal to 3 times the radius Step 1 Use the circumference to find the radius. C = 2πr 10π = 2πr r = 5 Circumference of a circle Substitute 10π for C. Divide both ...

original dimensions: length, width, and height doubled: S = Ph + 2B = 16 (3) + 2 (6) (2) = 72 in 2 S = Ph + 2B = 32 (6) + 2 (12) (4) = 288 in 2 Notice that 288 = 4 (72). If the length, width, and height are doubled, the surface area is multiplied by 2 2, or 4. 4. The height and diameter of the cylinder are multiplied ...

prism have Find the lateral area and surface area of each right prism. p. 681 2. 3. 4. a cube with edge length 9 inches. 682 Find the lateral area and surface area of each right cylinder. Give your answers in terms of π. 5. 6. 7. a cylinder with base area 64π m 2 and a height 3 meters less than the radius. 682 Multi-S...

ylinders 685 685 �� 24. Find the height of a right cylinder with surface area 160π ft 2 and radius 5 ft. 25. Find the height of a right rectangular prism with surface a...

. Round to the nearest tenth. 686 686 Chapter 10 Spatial Reasoning 10 ftge07sec10l04004aa1st pass4/23/5cmurphy10 ft10 ftge07sec10l04005a1st pass4/12/5cmurphy10 ft10 ft�� 38. Measure the dimensions of the net of a cylinder to the nearest millimeter. Which is closest to the surface area of the ...

right views of each object. Assume there are no hidden cubes. (Lesson 10-2) 48. 49. 50. 10- 4 Surface Area of Prisms and Cylinders 687 687 �� 10-4 Model Right and Oblique Cylinders In Lesson 10-4, you learned the difference between right and oblique cylinders. In this lab, you will make mode...

altitude of a pyramid vertex of a cone axis of a cone right cone oblique cone slant height of a right cone altitude of a cone Also G.5.A, G.5.B, G.6.B, G.11.D Why learn this? A speaker uses part of the lateral surface of a cone to produce sound. Speaker cones are usually made of paper, plastic, or metal. (See Example ...

__ 2 (2 √  3 ) (24) = 24 √  3 m 2. Step 2 Find the lateral area. Pℓ L = 1 _ 2 = 1 _ (24) (7) = 84 m 2 2 Step 3 Find the surface area. S = 1 _ 2 Pℓ + B Lateral area of a regular pyramid Substitute 24 for P and 7 for ℓ. Surface area of a regular pyramid = 84 + 24 √  3 ≈ 125.6 cm 2 Substitute 24 √  3 for B. 1. Find t...

agorean Theorem to find ℓ. ℓ = √  5 2 + 12 2 = 13 ft Step 2 Find the lateral area and surface area. L = πrℓ = π (5) (13) = 65π ft 2 S = πrℓ + π r 2 = 65π + π (5) 2 = 90π ft 2 Lateral area of a right cone Substitute 5 for r and 13 for ℓ. Surface area of a right cone Substitute 5 for r and 13 for ℓ. 2. Find the later...

(cone lateral area) + (cylinder lateral area) + (base area) = 2520π + 784π + 1484π = 4788π cm 2 4. Find the surface area of the composite figure. E X A M P L E 5 Electronics Application Electronics The paper cones of The paper cones of antique speakers were both functional and decorative. Some had elaborate patterns o...

effect of each change on the surface area of the given figure. p. 691 8. The dimensions are cut in half. 9. The dimensions are tripled Find the surface area of each composite figure. p. 692 10. 11. 692 12. Crafts Anna is making a birthday hat from a pattern that is 3 __ 4 of a circle of colored paper. If Anna’s head i...

is a regular square pyramid with the dimensions shown. a. Find the surface area of the container to the nearest tenth. b. The manufacturer decides to make a container in the shape of a right cone that requires the same amount of material. The base diameter must be 9 cm. Find the slant height of the container to the ne...