The height of a trazpezoid is 8 in. and its area is 96 in. square. One base of trapezoid is 6 inches longer thatn the other base. What are the lengths of the base?

Area of a trapezoid: is the average of the two base lenghts times the altitute.

base₁=x

base₂ = (x+6)

h=8 in

Area = [x + (x+6) / 2] * h

Therefore:

96 = [x + (x+6) / 2]*8

96=[ (2x+6) / 2]*8

96=8x+24

8x=96-24

8x=72

x=72/8=9

x+6=9+6=15

solution: The lengths of the bases ar 15 in and 9 in.

To chek:

A=[ (15 in + 9 in) / 2] * 8=96 in²