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

ABCD – isosceles trapezoid
AB = CD
BH = 16 – trapezoid height

Since in a given trapezoid the diagonals are mutually perpendicular, the height will be equal to half the sum of the bases of this trapezoid
h = a + b / 2
16 = a + b / 2
a + b = 16 * 2
a + b = 32

S = a + b / 2 * h
S = 32/2 * 16
S = 16 * 16
S = 256
256 cm ^ 2

Answer: 256 cm ^ 2 area of the trapezoid