Chapter 11.5, Problem 2CYU

To determine

To find: The area of the figure in green.

Answer to Problem 2CYU

The area of the given Figure is $78.4{\text{m}}^2$ .

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,

  $\begin{array}{l}{\left(\frac{5}{7}\right)}^2=\frac{40{\text{m}}^2}{x}\\ \frac{1}{x}=\frac{25}{49}\left(\frac{1}{40}\right)\\ x=\frac{40\left(49\right)}{25}\\ x=78.4{\text{m}}^2\end{array}$