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?

  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

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

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490