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?

The length of each side of tyhe nonagon is 16 units

Step-by-step explanation:

step 1

Find the perimeter of nonagon

we know that

The area of any regular polygon is given by the formula

where

P is the perimeter

a is the apothem

we have

substitute

solve for P

step 2

Find the length side of nonagon

we know that

The perimeter of nonagon is given by the formula

where

b is the length side of nonagon

we have

substitute

solve for b

  16 units

Step-by-step 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