Question

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

Answer 1

Answer:

Area of nonagon = 1044.6 square millimetres.

Step-by-step 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

$a=\frac{117}{9}$

$a=13$

So the side of the nonagon is 13

The area of the nonagon is .

$A=\frac{9}{4} a^{2} cot(\frac{180}{9})$

where a is side of the nonagon.

Put value of side in above equation

$A=\frac{9}{4} 13^{2} cot(20)$

$A=\frac{9\times 169}{4}\times 2.747}$

$A=\frac{1521}{4}\times 2.747}$

$A=380.25\times 2.747}$

$A=1044.55$

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