What is the area of an isosceles trapezoid if the length of an altitude is h, and diagonals are perpendicular to each other?

In order to answer that question, you have to work with right triangles in this ABCD trapezoid. Because of diagonals are perpendicular, we say that ΔAOD and  ΔBOC are right-isosceles triangles. ∠OBC= ∠FBD = 45°. Then, BF = FD = h. Similarly, in triangle ACE ∠ACE = 45°. From here, CE = AE = h. 

The area of this trapezoid is . We need to find AD and BC in order to calculate this area. Since we know that BC = FE. AE + FD = AD + BC. We know that AE + FD = 2h. 

The area is 

The first one is correct