The height of a trapezoid is 6 in. and its area is 36 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.

3 inches and 9 inches

Step-by-step explanation:

Area of a trapezoid is given by

A = 1/2 (b1+b2) * h where b1 and b2 are the lengths of the bases

b1 = b

b2 = b1+6 = b+6

h = 6

A = 36

Substituting in what we know

36 = 1/2 (b+b+6) * 6

Simplifying

36 = 3 (2b+6)

36/3 = 3/3 (2b+6)

Divide each side by 3

12 = 2b+6

Subtract 6 from each side

12-6 = 2b+6-6

6 = 2b

Divide each side by2

6/2 = 2b/2

3=b

b1 = b = 3

b2 = b1+6 = b+6 = 3+6 = 9

One base is 3 and the other is 9