The height of a trapezoid is 8 in. And its area is 64 in2. One base of the trapezoid is 6 inches longer than the other base. What are the lengths of the bases?

5 and 11

Step-by-step explanation:

The area of a trapezoid is

A = 1/2 (b1+b2) * h

We know the height is 8 and the area is 64.

Let one of the bases is b and the other is b+6

64 = 1/2 (b + b+6) * 8

Combine like terms

64 = 4 (2b+6)

Divide each side by 4

64/4 = 4/4 * (2b+6)

16 = 2b+6

Subtract 6 from each side

16-6 = 2b+6-6

10 = 2b

Divide each side by2

10/2 = 2b/2

5=b

The second base is

5+6 = 11