Chapter 11.5, Problem 6PPS

To determine

To find: The area of the green figure.

Answer to Problem 6PPS

The area of the second Figure is $81{\text{mm}}^2$ .

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,

  $\begin{array}{l}{\left(\frac{18}{10}\right)}^2=\frac{A}{25}\\ A={\left(\frac{18}{10}\right)}^{2}25\\ A=81{\text{mm}}^2\end{array}$