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

Identify the area of a regular nonagon with side length 18 cm. Round to the nearest-example-1
User Michelli
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1 Answer

4 votes

Answer:


A=2,002.9\ cm^(2)

Explanation:

we know that

The area of a regular polygon is equal to


A=(1)/(2)rP

where

r is the apothem

P is the perimeter

step 1

Find the perimeter

The perimeter of a regular nonagon is


P=ns

where

n is the number of sides (n=9)

s is the length side (s=18 cm)

substitute


P=9*18=162\ cm

step 2

Find the apothem

The apothem in a regular polygon is equal to


r=(1)/(2)(s)cot(180\°/n)

we have


s=18\ cm


n=9

substitute


r=(1)/(2)(18)cot(180\°/9)


r=9cot(20\°)=24.73\ cm

step 3

Find the area of the regular nonagon


A=(1)/(2)rP

substitute


A=(1)/(2)(24.73)(162)=2,002.9\ cm^(2)

User Joe Haddad
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