Chapter 13.1, Problem 17PSB

To determine

To find: The area of the shaded region to the nearest tenth.

Answer to Problem 17PSB

The area of the shaded region is $21.46$ square unit.

Explanation of Solution

Given:

The given diagram is as follows.

  

Calculation:

Find the area of the square.

  $\begin{array}{c}{A}_S=10\times 10\\ =100\end{array}$

Find the area of the circle.

  $\begin{array}{c}{A}_C=\pi r^2\\ =\pi {\left(5\right)}^2\\ =78.54\end{array}$

Subtract the area of the circle from the area of the square to find the area of the shaded region.

  $\begin{array}{c}A=A_S-A_C\\ =100-78.54\\ =21.46\end{array}$

Therefore, the area of the shaded region is $21.46$ square unit.