Chapter 14, Problem 10MCE

To determine

Tofind: the ratio of the area of regular octagons.

Answer to Problem 10MCE

The ratio of the area of regular octagonsis $4:3$ .

Explanation of Solution

Given information:

The sides of regular octagons are $6\sqrt{3}\text{ and }9$ .

Calculation: to find ratio of the areas of octagons,

$\begin{array}{l}\frac{A_1}{A_2}=\frac{2a_1{}^2}{2a_2{}^2}\\ \frac{A_1}{A_2}=\frac{{\left(6\sqrt{3}\right)}^2}{{\left(9\right)}^2}\text{ [substitute]}\\ \frac{A_1}{A_2}=\frac{108}{81}\text{ [multiply]}\\ \frac{A_1}{A_2}=\frac{4}{3}\text{ [simplify]}\end{array}$

Thus, Theratio of the area of regular octagons is $4:3$ .