Question

The height of a trapezoid is 6 in. And its area is 48 in2. One base of the trapezoid is 6 inches longer than the other base. What are the lengths of the bases? Complete the explanation of how you found your answer.

Answer 1

• 5 in
• 11 in

Explanation:

Let x represent the length of the shorter base in inches. Then the longer base has length x+6. The area of the trapezoid is given by the formula ...

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

Filling in the values we know, we have ...

48 = (1/2)(x +(x+6))(6)

16 = 2x +6 . . . . . divide by 3

10 = 2x . . . . . . . . subtract 6

5 = x . . . . . . . . . . divide by 2

(x+6) = 11 . . . . . . find the longer base

The lengths of the bases are 5 inches and 11 inches. We found them by solving an equation relating area to base length.