Chapter 11.5, Problem 5CYU

To determine

To find: The area of the small opening.

Answer to Problem 5CYU

The area of the smaller opening is $5.28{\text{in}}^2$ .

Explanation of Solution

Given:

The area of the centre opening is $36{\text{in}}^2$ .

The given Figure 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 smaller opening is,

  $\begin{array}{l}{\left(\frac{1.2}{3}\right)}^2=\frac{A}{33}\\ A=33{\left(\frac{1.2}{3}\right)}^2\\ A=5.28{\text{in}}^2\end{array}$