Question

The area of a trapezoid is 30 square centimeters. The height is 4 centimeters. The shorter base measures 6 centimeters. What is the measure of the longer base? Draw a picture of the problem. Explain your thinking,

Answer 1

The measure of the longer base is:

9 centimeters

Explanation:

We know that the area of a trapezoid with height h and two parallel bases b and b' is given by the formula:

`\text{Area of trapezoid}=(1)/(2)* (b+b')* h`

Here we have:

The area of a trapezoid is 30 square centimeters. The height is 4 centimeters. The shorter base measures 6 centimeters.

i.e.

`30=(1)/(2)* (b+6)* 4\\\\30=2(b+6)\\\\b+6=(30)/(2)\\\\b+6=15\\\\b=15-6\\\\b=9\ \text{centimeters}`

Answer 2

The measure of the longer base is
`9\ cm`

The picture of the problem in the attached figure

Explanation:

we know that

The area of a trapezoid is equal to

`A=(1)/(2)(b1+b2)h`

where

b1 ----> the measure of the shorter base

b2 ----> the measure of the longer base

h ---> is the height

In this problem we have

`A=30\ cm^(2)`

`b1=6\ cm`

`h=4\ cm`

substitute the values and solve for b2

`30=(1)/(2)(6+b2)4`

`15=(6+b2)`

`b2=15-6=9\ cm`