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can someone answer how to find the height of a trapezoid without the area
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You have to know other things. For example, you can find the height using component triangles within the trapezoid, using the sin functions.
Can you show a picture? Sorry. I don't grasp what you mean by the legs so to speak of the isosceles triangle.
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What is that 5 on the one side of the trapezoid trying to present? If you know the perimeter of the Trapezoid, and you know the length of at least 3 sides, you can find the length of the missing side by subtracting the three sides.
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