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

Answer:

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

Step-by-step 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

$P = 9*s\\135 = 9*s\\s = \frac{135}{9}\\s = 15\ inches$

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

$A = \frac{a*n*s}{2}\\A = \frac{6*9*15}{2}\\A=\frac{810}{2}\\A = 405\ in^2$

Also the formula can be written as:

$A = \frac{1}{2}P*a$

Hence,

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