Find the area of an isosceles trapezoid whose height is 16 cm and the diagonals are mutually perpendicular.

We recall the theorem according to which if in an isosceles trapezoid the diagonals are mutually perpendicular, then its height is equal to the half-sum of the bases. Therefore, the half-sum of the bases is 16 cm.
The area of the trapezoid is found as the product of the half-sum of the bases and the height. We know all the data, we calculate the area:
S = 16 * 16 = 256 cm2 – the area of an isosceles trapezoid.
Answer: The area of an isosceles trapezoid is 256 cm2.