Chapter 11.5, Problem 20PSC

a

To determine

To calculate: The apothem of regular octagon with side 10.

Answer to Problem 20PSC

Apothem of regular octagon $\frac{5}{\sqrt{2}-1}$ units.

Explanation of Solution

Given information :

One side of octagon ( s ) = $10$ .

Formula used: Apothem of polygon = $\frac{s}{2\tan \left(\frac{180}{n}\right)}$

where “ s ” is length of side and “ n ” is number of sides

Calculation: Apothem of octagon $=\frac{10}{2\tan \left(\frac{180}{8}\right)}$

  $\begin{array}{l}\Rightarrow \frac{5}{\tan (22.5)}\\ \Rightarrow \frac{5}{\sqrt{2}-1}\end{array}$

b

To determine

To calculate: The area of regular octagon with side $10$ .

Answer to Problem 20PSC

Area of regular octagon $200(1+\sqrt{2}){\text{ units}}^2$ .

Explanation of Solution

Given information :

One side of octagon ( a ) = $10$ .

Formula used: Area of regular octagon = $2(1+\sqrt{2})a^2$ (where a is the length of side)

Calculation: Area of regular octagon = $2(1+\sqrt{2}){(10)}^2$

  $\begin{array}{l}$ \Rightarrow 2(1+\sqrt{2}){(10)}^2$\Rightarrow 2(1+\sqrt{2})(100)\\ \Rightarrow 200(1+\sqrt{2})\end{array}$