Question

Find the area of a regular polygon with 9 sides that has a perimeter of 135 inches and an apothem of 6 inches

Answer 1

The area of regular polygon with 9 sides is 405 square inches.

Explanation:

Given

Perimeter of Polygon = P = 135 inches

Apothem = a = 6 inches

We know that the sides of regular polygon are equal. Let s be the side of the polygon then

`P = 9*s\\135 = 9*s\\s = (135)/(9)\\s = 15\ inches`

Now the formula for area of polygon when apothem, sides and number of sides is known:

`A = (a*n*s)/(2)\\A = (6*9*15)/(2)\\A=(810)/(2)\\A = 405\ in^2`

Also the formula can be written as:

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

Hence,

The area of regular polygon with 9 sides is 405 square inches.