Chapter 11.5, Problem 8PPS

To determine

To find: The area of the green figure.

Answer to Problem 8PPS

The area of the green Figure is $151.25{\text{in}}^2$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Two polygons are similar only when the corresponding angles are equal and congruent and corresponding side length are in proportion.

Consider the formula to determine the scale factor is,

  $k^2=\frac{A_1}{A_2}$

As both the figure are similar then the area of the green figure that is figure on the right is,

  $\begin{array}{l}{\left(\frac{15.4}{28}\right)}^2=\frac{A}{500{\text{in}}^2}\\ A={\left(\frac{15.4}{28}\right)}^{2}500{\text{in}}^2\\ A=151.25{\text{in}}^2\end{array}$