Question

What is the area? Round to the nearest tenth if necessary.

Answer 1

`\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=na^2\cdot \tan\left( (180)/(n) \right) ~~ \begin{cases} n=sides\\ a=apothem\\[-0.5em] \hrulefill\\ n=8\\ a=17 \end{cases}\implies A=(8)(17)^2\tan\left( (180)/(8) \right) \\\\\\ A=2312\tan(22.5^o)\implies A\approx 957.7`

Make sure your calculator is in Degree mode.

Answer 2

Set your calculator to degree mode.

Draw a line from point O to a vertex of this octagon to form a right triangle.

tan(67.5°) = 17/x, so x = 17/tan(67.5°)

Area = (1/2)(34/tan(67.5°))(8)(17) = 957.7