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An isosceles trapezoid has parallel sides of length 10 and 25, with legs of length 15. Find the area of the trapezoid when the angle between one leg and the shorter side is 45 degrees. | ai2-adapt-dev/openmath-2-math | **Given:**
- Isosceles trapezoid with:
- Parallel sides (bases) \(AB = 10\) (shorter side) and \(CD = 25\) (longer side)
- Legs \(AD = BC = 15\)
- One leg forms a \(45^\circ\) angle with the shorter base
---
### Step 1: Understand the setup
Let the trapezoid be \(ABCD\) with \(AB \parallel CD\), \(AB = 10\), \(C... | 179,672 | 7,647 | 1 | <think>
Okay, so I need to find the area of an isosceles trapezoid. The problem says it has parallel sides of length 10 and 25, and the legs are 15 each. Also, there's a specific angle given: the angle between one leg and the shorter side is 45 degrees. Hmm, let me recall how to approach this.
First, the formula for t... | <think>
Okay, so I need to find the area of an isosceles trapezoid. The trapezoid has two parallel sides, called the bases, with lengths 10 and 25 units. The legs, which are the non-parallel sides, are each 15 units long. Additionally, the angle between one leg and the shorter base (the side of length 10) is 45 degrees... | [
{
"from": "human",
"value": "An isosceles trapezoid has parallel sides of length 10 and 25, with legs of length 15. Find the area of the trapezoid when the angle between one leg and the shorter side is 45 degrees."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the area of an iso... |
"A bookstore has 5 shelves, each with a different genre of books: fiction, non-fiction, biographies,(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's analyze the problem step-by-step.\n\n**Given:**\n- 5 shelves, each with a different genre:\n (...TRUNCATED) | 244,962 | 3,994 | 3 | "<think>\nOkay, so there's this bookstore with 5 shelves, each for a different genre: fiction, non-f(...TRUNCATED) | "<think>\nOkay, so there's this problem about a bookstore with 5 shelves, each having a different ge(...TRUNCATED) | [{"from":"human","value":"A bookstore has 5 shelves, each with a different genre of books: fiction, (...TRUNCATED) |
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