Answer:
Height = 10 inches
Length of the bases are
base1 = 20 inches
base2 = 12 inches
Explanation:
Given that the area of trapezoid = 160 inches²
Let base1 and base2 represent the trapezoid bases respectively.
Sum of base1 and base2 = 32 inches.
base1 + base2 = 32 inches
One base of the trapezoid is 8 inches longer than the other base.
Let assume base1 is the longer base:
base1 = base2 + 8
1) what is the height?
From the formula of area of trapezoid
Area = 1/2 x height x sum of bases.
Therefore
160 = 1/2 x height x 32
160 = 16 x height
Height = 160/16 = 10 inches.
2) What are the lengths of the bases?
Given that, sum of bases = 32 inches
:. base1 + base2 = 32
And base1 = base2 + 8
base1 + base2 = 32 will be equivalent to
base2 + 8 + base2 = 32
2(base2) + 8 = 32
base2 = (32-8)/2
base2 = 12 inches
And
base1 = base2 + 8
base1 = 12+8
base1 = 20 inches