Chapter 11.4, Problem 19PPS

To determine

To find: The area of each figure.

Answer to Problem 19PPS

The area of figure is $42.1{\text{yd}}^2$ .

Explanation of Solution

Given:

The given figure is:

  

Calculation:

To find the area of the figure, subtract the area of the circle from the area of the square.

Area of square with dimension $14\text{yd}\times 14\text{yd}$ is calculated as:

  $\begin{array}{c}\text{Area}={\left(\text{side}\right)}^2\\ ={\left(14\right)}^2\\ =196\end{array}$

Area of the circle with radius $7\text{yd}$ is calculated as:

  $\begin{array}{c}\text{Area}=\pi r^2\\ \approx \left(3.14{\left(7\right)}^2\right)\\ \approx 153.86\end{array}$

Area of shaded region is calculated as:

  $\begin{array}{c}\text{Area of figure}=\text{Area of square}-\left(\text{Area of circle}\right)\\ \approx 196-153.86\\ \approx 42.1\end{array}$

Therefore the area of figure is $42.1{\text{yd}}^2$ .