Identify the area of a regular nonagon with side length 18 cm. Round to the nearest tenth. HELP ASAP PLEASE!!

Accepted Solution

Answer:[tex]A=2,002.9\ cm^{2}[/tex]Step-by-step explanation:we know thatThe area of a regular polygon is equal to[tex]A=\frac{1}{2}rP[/tex]wherer is the apothemP is the perimeterstep 1Find the perimeterThe perimeter of a regular nonagon is [tex]P=ns[/tex]wheren is the number of sides (n=9)s is the length side (s=18 cm)substitute[tex]P=9*18=162\ cm[/tex]step 2Find the apothemThe apothem in a regular polygon is equal to[tex]r=\frac{1}{2}(s)cot(180\°/n)[/tex]we have[tex]s=18\ cm[/tex][tex]n=9[/tex]substitute[tex]r=\frac{1}{2}(18)cot(180\°/9)[/tex][tex]r=9cot(20\°)=24.73\ cm[/tex]step 3Find the area of the regular nonagon[tex]A=\frac{1}{2}rP[/tex]substitute[tex]A=\frac{1}{2}(24.73)(162)=2,002.9\ cm^{2}[/tex]