Chapter 11.4, Problem 29PPS

To determine

To find: The area of the shaded region.

Answer to Problem 29PPS

The area of the composite figure is $19.7{\text{sq}}^{\text{2}}$ .

Explanation of Solution

Given:

The given figure is shown in Figure 1

  

Figure 1

Calculation:

Consider the area of the composite figure is of the form,

  $A=A_{\text{rectangle}}-A_{\text{trapezoid}}-A_{\text{semicircle}}$

Then,

  $\begin{array}{c}A=4\left(8\right)-\frac{1}{2}\left(2+4\right)\left(2\right)-\frac{1}{2}\pi {\left(2\right)}^2\\ =32-6-2\pi \\ =19.7{\text{sq}}^{\text{2}}\end{array}$