Chapter 11.3, Problem 20PPS

To determine

To calculate: The area of the shaded region.

Answer to Problem 20PPS

The area of the shaded region is $167.1f{t}^2$ .

Explanation of Solution

Given information: The radius of the circle is $12ft$ . Degree of the arc is ${133}^{\circ }$ .

Calculation:

From the given information, radius, $r=12ft$ .

Degree of arc, $x={133}^{\circ }$ .

Area of a sector is given by, $A=\pi r^2\times \frac{x}{360}$

  $\begin{array}{l}A=\pi {12}^2\times \frac{133}{360}\\ A=144\pi \times \frac{133}{360}\\ A=167.10\end{array}$

Area of shaded region, $A=167.1f{t}^2$

The area of the shaded region is $167.1f{t}^2$ .