Question

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

Answer 1

`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)`