Chapter 11.4, Problem 30PPS

To determine

To find: The area of the shaded region.

Answer to Problem 30PPS

The area of the composite figure is $19.9$ .

Explanation of Solution

Given:

The given figure is shown in Figure 1

  

Figure 1

Calculation:

Consider the figure is in the shape of the kite with the two semicircle.

Then, the diameter of the semicircle is,

  $\begin{array}{c}d=\sqrt{3^2+1^2}\\ =\sqrt{10}\end{array}$

The radius is,

  $r=\frac{\sqrt{10}}{2}$

Then, the area of the composite figure is,

  $\begin{array}{c}A=\frac{1}{2}{d}_1{d}_2+2\left(\pi r^2\right)\\ =\frac{6\cdot 4}{2}+2\left(\frac{1}{2}\pi {\left(\frac{\sqrt{10}}{2}\right)}^2\right)\\ =12+\frac{5}{2}\pi \\ \approx 19.9\end{array}$