Question

The height of a trapezoid is 6 in. and its area is 72 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

Formula
Area = (B1 + B2)*h/2
Area = 72 in²
B1 = x
B2 = x +6
h = 6 in

Substitute and Solve
Area = (x + 6 + x)*6/2  = 72 Divide by 2
Area = (2x + 6)*3 = 72 Remove the brackets
Area = 6x + 18 = 72 Subtract 18
6x = 72 - 18 
6x = 66 Divide by 6
x = 66/6
x = 11

B1 and B2
Base 1 = 6
Base 2 = 12

Answer 2

Let x in be the length of smaller base, then greater base has length x+6 in. The midline of trapezoid is

$\dfrac{x+x+6}{2}=\dfrac{2x+6}{2}=x+3.$

You can find the area of trapezoid using formula

$A=\text{midline}\cdot \text{height}.$

Then

$72=(x+3)\cdot 6,\\ \\x+3=\dfrac{72}{6},\\ \\x+3=12,\\ \\x=12-3,\\ \\x=9\ in.$

Answer: the smaller base has length x=9 in and the greater base has length x+6=9+6=15 in.