Question

find the area of the trapezoid whose diagonals are 30 each and height of 18?

I spent 2 hrs and I can't figure it out Pls. help
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Answer 1

Who says this trapezoid is not a rectangle with height 18 and base sqrt (30^2-18^2)?

Answer 2

1. extend the top line of the trapezoid to the left, to make a right triangle with the top line and the diagonal.
2. This triangle has side of 18 and hypotenuse of 30. By pythagorean theorem, the extended top line is 24.
3. Draw a line from upper right point of trapezoid to base, making a another 18x24x30 triangle.
4. The area of the trapezoid is 18x24 = 432, which is the area of the rectangle formed from the 2 triangles.
5. The small triangles (one inside the rectangle upper left and one outside of the rectangle lower left) are congruent.