Exercise 49 Page 847

Find the area of the rectangle and the area of a circle.

About 30.37 square centimeters

Practice makes perfect

Let's analyze the given shaded region.

We are asked to find its area. Notice that it is equal to the difference between the area of the rectangle and the area of the circle.

c Area of Region = c Area of Rectangle - c Area of Circle Since the sides of the rectangle are 5 and 10 centimeters, its area is 5* 10= 50 square centimeters. The radius of the circle is half of the shorter side of the rectangle. Therefore, r= 52=2.5 centimeters. Now, we can use the formula for the area of a circle.

A_\text{circle}=\pi r^2

Substitute

r= 2.5

A_\text{circle}=\pi ({\color{#009600}{2.5}})^2

CalcPowProd

Calculate power and product

A_\text{circle}=6.25\pi

Finally, let's find the area of the shaded region. c Area of Region = c Area of Rectangle - c Area of Circle ⇓ c Area of Region = 50- 6.25π This tells us that the area of the shaded region is 50-6.25π square centimeters. Let's approximate the answer.

A_\text{region}=50-6.25\pi

UseCalc

Use a calculator

A_\text{region}=30.365045\ldots

RoundDec

Round to 2 decimal place(s)

A_\text{region}\approx 30.37

Finally, the area of the shaded region is about 30.37 square centimeters.

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