Question

a trapezoid abcd has parallel sides ab and dc of lengths 8 and 22. If both diagonals AC and BD are of length 17, what is the area of the trapezoid

Answer 1

the excess length of dc over ab is 22-8=14

SO, there are two triangles of base 7 and hypotenuse 17 at the ends of the trapezoid.

The height h of the trapezoid is thus

h^2 = 17^2 - 7^2 = 240
h = √240

The area of the trapezoid

A = (8+22)/2 * √240
= 15*4√15 = 60√15

Answer 2

Oops. I was considering the 17 as the length of the edges, not the diagonals.

The height h is given by

15^2 + h^2 = 17^2
h=8

A = (8+22)/2 * 8 = 120