Question

A regular nonagon (9 sides) has an area of 1582.56 square units. If the length of the apothem is about 21.98 units, how long would each side of the nonagon be?

Answer 1

16 units

Explanation:

The area is given by ...

A = (1/2)Pa

Then the perimeter (P) is ...

1582.56 = (1/2)(21.98)P

P = 1582.56/10.99 = 144

The perimeter is 9 times the side length, so each side is ...

144 units/9 = 16 units . . . . length of one side

Answer 2

The length of each side of tyhe nonagon is 16 units

Explanation:

step 1

Find the perimeter of nonagon

we know that

The area of any regular polygon is given by the formula

`A=(1)/(2)P(a)`

where

P is the perimeter

a is the apothem

we have

`A=1.582.56\ units^2`

`a=21.98\ units`

substitute

`1,582.56=(1)/(2)P(21.98)`

solve for P

`P=144\ units`

step 2

Find the length side of nonagon

we know that

The perimeter of nonagon is given by the formula

`P=9b`

where

b is the length side of nonagon

we have

`P=144\ units`

substitute

`144=9b`

solve for b

`b=16\ units`