Question

6. Find the area of the regular nonagon.
0.94
1
PLEASE HELP!

Answer 1

we could go ahead and use the pythagorean theorem to get the length of a side blah blah and get the area with the apothem of 0.94, or we can just use the apothem alone all by itself

`\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=na^2\tan((180)/(n)) ~~ \begin{cases} n=sides\\ a=apothem\\[-0.5em] \hrulefill\\ n=9\\ a=0.94 \end{cases}\implies A=(9)(0.94)^2\tan((180)/(9)) \\\\\\ A=(9)(0.94)^2\tan(20^o)\implies A\approx 2.89~units^2`

Make sure your calculator is in Degree mode.