Chapter 11.4, Problem 6CE

To determine

To Find: Perimeter, measure of central angle, apothem $a$ , radius $r$ and the area $A$ .

Answer to Problem 6CE

  $P=16$

Central angle:

  $m\angle AOB={90}^{°}$

  $a=2$

  $r=2\sqrt{2}$

  $A=16sq.unit$

Explanation of Solution

Given:

  

  

Here $s=4$

(a)Perimeter

  $\begin{array}{l}P=ns\\ n=4\\ i.e.\\ P=4(4)\\ P=16\end{array}$

(b) Measure of central angle.

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

(c) Apothem

  $\begin{array}{l}m\angle AOX=\frac{1}{2}m\angle AOB=\frac{{90}^{°}}{2}={45}^{°}\\ In\Delta AOX\\ \angle AOX=\frac{AX}{OX}=\frac{2}{a}=1\\ a=2\end{array}$

(d) Radius

  $\begin{array}{l}In\Delta AOX\\ \sin \angle AOX=\frac{AX}{OA}=\frac{2}{r}=\frac{1}{\sqrt{2}}\\ r=2\sqrt{2}\end{array}$

(e) Area

  $\begin{array}{l}A=\frac{1}{2}aP\\ A=\frac{1}{2}(2)(16)\\ A=16sq.unit\end{array}$