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

Answer:

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

The picture of the problem in the attached figure

Step-by-step explanation:

we know that

The area of a trapezoid is equal to

$A=\frac{1}{2}(b1+b2)h$

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

$30=\frac{1}{2}(6+b2)4$

$15=(6+b2)$

$b2=15-6=9\ cm$

Answer 2

Answer:

The measure of the longer base is:

                            9 centimeters

Step-by-step explanation:

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

$\text{Area of trapezoid}=\dfrac{1}{2}\times (b+b')\times h$

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.  

$30=\dfrac{1}{2}\times (b+6)\times 4\\\\30=2(b+6)\\\\b+6=\dfrac{30}{2}\\\\b+6=15\\\\b=15-6\\\\b=9\ \text{centimeters}$