Chapter 13.7, Problem 3PSA

(a)

To determine

To find:The area of the shaded region

Answer to Problem 3PSA

The area of the shaded region is $16.7\text{sq}\text{.}\text{units}$ .

Explanation of Solution

The area of the shaded region is calculated as,

  $\begin{array}{c}{A}_{\text{shaded}}=A_{\text{square}}-A_{\text{circle}}\\ ={\left(8\right)}^2-\pi {\left(4\right)}^2\\ =64-16\pi \\ =16.7\text{sq}\text{.units}\end{array}$

Therefore, the area of the shaded region is $16.7\text{sq}\text{.}\text{units}$ .

(b)

To determine

To find: The area of the shaded region

Answer to Problem 3PSA

The area of the shaded region is $30.5\text{sq}\text{.}\text{units}$ .

Explanation of Solution

The area of the shaded region is calculated as,

  $\begin{array}{c}{A}_{\text{shaded}}=A_{\text{circle}}-A_{\text{rectangle}}\\ =\pi {\left(5\right)}^2-\left(6\right)\left(8\right)\\ =25\pi -48\\ =30.5\text{sq}\text{.units}\end{array}$

Therefore, the area of the shaded region is $30.5\text{sq}\text{.}\text{units}$ .