Chapter 11.4, Problem 35HP

To determine

To find: The correct area of the polygon.

Answer to Problem 35HP

The correct answer is of Chloe.

Explanation of Solution

Given:

The given Figure is shown in Figure 1

  

Figure 1

The area of the polygon by Chloe is,

  $\begin{array}{c}A=\frac{1}{2}Pa\\ =\frac{1}{2}\left(66\right)\left(9.5\right)\\ =313.5{\text{in}}^2\end{array}$

Then, the area of the flavio is,

  $\begin{array}{c}A=\frac{1}{2}Pa\\ =\frac{1}{2}\left(33\right)\left(9.5\right)\\ =156.8{\text{in}}^2\end{array}$

Calculation:

The hexagon has three sides, then the measure of the central angle is,

  $\frac{360}{6}=60°$

Since, the regular hexagon as $s=11\text{in}$ . Then,

  $\begin{array}{c}P=6\left(11\right)\\ =66\text{in}\\ =\text{313}\text{.5}\text{in}\end{array}$

Consider the law of cosine as,

  $\begin{array}{l}\sin 60°=\frac{a}{11}\\ a=11\sin 60°\\ a=9.5\end{array}$

Thus, the correct answer is of Chloe.