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
[tex]P = 9*s\\135 = 9*s\\s = \frac{135}{9}\\s = 15\ inches[/tex]
Now the formula for area of polygon when apothem, sides and number of sides is known:
[tex]A = \frac{a*n*s}{2}\\A = \frac{6*9*15}{2}\\A=\frac{810}{2}\\A = 405\ in^2[/tex]
Also the formula can be written as:
[tex]A = \frac{1}{2}P*a[/tex]
Hence,
The area of regular polygon with 9 sides is 405 square inches.
