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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,

User Luck
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6.1k points

2 Answers

5 votes

Answer:

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}

The area of a trapezoid is 30 square centimeters. The height is 4 centimeters. The-example-1
User Ranjeetcao
by
6.8k points
1 vote

Answer:

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

The area of a trapezoid is 30 square centimeters. The height is 4 centimeters. The-example-1
User Makan
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6.4k points