Chapter 13.3, Problem 52SR

To determine

To calculate:

The area of shaded region of given figure.

Answer to Problem 52SR

The area of shaded region is $104.8i{n}^2$ .

Explanation of Solution

Given information:

  

Calculation:

A shaded square contains $4$ unshaded circles each with a radius of $7$ inches.

The square has an area equal to $\left(7in\right)\left(7in\right)=49i{n}^2$ and the circle has an area equal to,

  $\pi {\left(7in\right)}^2=153.8i{n}^2$

The area of the shaded region is found by subtracting the area of the circle from the area of the square.

  $\begin{array}{l}\text{Shaded region area}=\text{area of square-area of circle}\\ \text{=}49i{n}^2-153.8m^2\\ =104.8i{n}^2\end{array}$

Hence the area of shaded region is $104.8i{n}^2$ .