Take The Trapezoid Quiz

Trapeziod ABCD: Find Trapeziod Area

AB  ||  DC

The bases of the trapezoid, AB and DC are given.

The height of the trapeziod, h, needs to be determined.

The height (h) from B to EC froms a leg shared by two right triangles: BDE and BCE

\(x^2 + h^2 = 169\quad \text{for triangle BCE} \)

\((21-x)^2 + h^2 = 400\quad \text{for triangle BDE}\)

HINT: The hypotenuse is specified for both right triangles. Hypotenuse for BDE = 20, hypotenuse for BCE = 13. By subtracting the first equation from the second the problem is simplified for finding x. Once x is known each of the two triangles are then solved.

1. Calculate the height, h:

2. Calculate the distance, x: