Chapter 11, Problem 29SGR

To determine

To find: The area of the stop sign in square inches.

Answer to Problem 29SGR

The area of regular octagon is $695.23{\mathrm{inches}}^2$ .

Explanation of Solution

Given information: Side of regular octagon is $1ft$ .

Calculation: Side of regular octagon is $1ft$ .

  $1ft=12\mathrm{inch}$

So side of regular octagon $=12\mathrm{inch}$ .

Area of regular octagon:

  $\begin{array}{l}=2\left(1+\sqrt{2}\right)a^2\\ =2\left(1+\sqrt{2}\right){\left(12\right)}^2\\ =2\left(1+1.414\right)(144)\\ =2(2.414)(144)\\ =(4.828)(144)\\ =695.23{\mathrm{inches}}^2\end{array}$

Thus the area of regular octagon is $695.23{\mathrm{inches}}^2$ .