Question

Find the area : a nonagon with a perimeter of 117 millimeters

Answer 1

Area of nonagon = 1044.6 square millimetres.

Explanation:

Let side of the nonagon is a

Given:

The perimeter of nonagon is 117 millimetres

`perimeter=9a`

Put the perimeter value in above equation

`a=(117)/(9)`

`a=13`

So the side of the nonagon is 13

The area of the nonagon is .

`A=(9)/(4) a^(2) cot((180)/(9))`

where a is side of the nonagon.

Put value of side in above equation

`A=(9)/(4) 13^(2) cot(20)`

`A=(9* 169)/(4)* 2.747}`

`A=(1521)/(4)* 2.747}`

`A=380.25* 2.747}`

`A=1044.55`

Therefore, the area of the nonagon is 1044.6 square millimetre.