We are given the area of an isosceles trapezoid which is 72 m^2 and its diagonals are perpendicular. We need to find the length of a diagonal.
The formula for the area of an isosceles trapezoid is:
A = 1/2 (b1+b2) h
Solve for the sides and the bases of the trapezoid and then solve for the length of the diagonal,
d = √((b1 * b2) + h^2)