Question

The height of a trapezoid is 4 in. And its area is 48 in 2. One base of the trapezoid is 6 inches longer than the other base. What are the length of the bases? Complete the explanation on how you found your answer

Answer 1

Answer:

9 inches and 15 inches

Step-by-step explanation:

The height of a trapezoid is 4 in.

Its area is 48 in^2.

Let a be one base and b be the second base.

One base is 6 inches longer than the other. This implies that:

a = 6 + b _________ (1)

The formula for the area of a trapezoid is given as:

$A = \frac{1}{2}(a + b)h$

where h = height

From (1), we have that:

$A = \frac{1}{2}(6 + b + b )h\\ \\A = \frac{1}{2}(6 + 2b )h$

We have that h = 4 and A = 48 in^2, therefore:

$48 = \frac {1}{2}(6 + 2b) * 4\\ \\96 = 24 + 8b\\\\8b = 96 - 24 = 72\\\\b = 72 / 8 = 9 in$

=> a = 6 + 9 = 15 in

The bases are 9 inches and 15 inches long.