In trapezoid ABCD segments AB and CD are parallel. Point P is the intersection of diagonals AC and BD. The area of APAB is 16 square units, and the area of ▲PCD is 25 square units. What is the area of trapezoid ABCD?

Guest Aug 26, 2023

#1**0 **

Since triangles APAB and PCD are both right triangles, and they share the hypotenuse AP, they are similar triangles. Let x be the length of AP. Then the length of PB is x, the length of PC is 5x, and the length of PD is 4x.

The area of trapezoid ABCD is:

(1/2)(x + 4x)(5x) = 15x^2 = 15(16) = 240 square units

Guest Aug 26, 2023