Chapter 11.4, Problem 1WE

To determine

To Find: Apothem $a$ and the area $A$ .

Answer to Problem 1WE

  $a=8$

  $A=256sq.unit$

Explanation of Solution

Given:

  

Measure of central angle.

  $\begin{array}{l}m\angle COD=\frac{{360}^{°}}{n}=\frac{360}{4}\\ m\angle COD={90}^{°}\end{array}$

  $COD$ is an isosceles triangle.

Now

  $\begin{array}{l}OD=\sqrt{2}ON\\ ON=\frac{OD}{\sqrt{2}}\\ a=8\end{array}$

Now according to mid-point theorem

  $\begin{array}{l}DN=\frac{1}{2}DC\\ DC=2DN\\ DC=2(8)\\ DC=16\end{array}$

Thus perimeter

  $\begin{array}{l}p=4DC\\ p=4(16)\\ p=64\end{array}$

Now area

  $\begin{array}{l}A=\frac{1}{2}ap\\ A=\frac{1}{2}(8)(64)\\ A=256sq.unit\end{array}$