Answer:
[tex]A=2,002.9\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of a regular polygon is equal to
[tex]A=\frac{1}{2}rP[/tex]
where
r is the apothem
P is the perimeter
step 1
Find the perimeter
The perimeter of a regular nonagon is
[tex]P=ns[/tex]
where
n is the number of sides (n=9)
s is the length side (s=18 cm)
substitute
[tex]P=9*18=162\ cm[/tex]
step 2
Find the apothem
The 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 3
Find 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]
