Question

Find the area of a regular polygon with 9 sides that has a side length of 12 inches and an apothem of 15 inches.​

Answer 1

An apothem is a line drawn from the centerpoint of the polygon to one side of the polygon. There is a formula for area in terms of apothem:

A = (1/2)*(Perimeter)*(Apothem)

The perimeter of the regular polygon is just the length of one side multiplied with the number of sides. Since a polygon with 9 sides,

P = 9(15) = 135in

A = 1/2 ×135 × 12

A = 810 square inches ans