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
