Trapezoid ABCD has right angles at A and D, and diagonals AC and DB intersect at point E. The area of triangle ABE is 25 square units, and the area of triangl

Question

Trapezoid ABCD has right angles at A and D, and diagonals AC and DB intersect at point E. The area of triangle ABE is 25 square units, and the area of triangle DEC is 49 square units. If AD equals 6, what is the area of trapezoid ABCD.

Answer 1

 Triangles ABE and CDE are similar. So the sides are proportional. They are in the ratio Sqrt(25/49) =5/7 Use this and the area op the triangles to find the sides AB and CD. Then find the area of the trapezoid.