Area Regular Polygon

Definition: An apothem of a regular polygon is any perpendicular line segment drawn from the center of the polygon to a side that forms a right angle with that side. Area of a regular polygon is A = ap/2 where A is the area of the polygon, a is the apothem of the polygon, and p is the perimeter of the polygon.

Teaser: The teledrive housing in Raspune’s ship is in the shape of a regular decagon with a side of 10 meters. the apothem is 15.39. What is the area of the decagon?

Example : Find the area of a regular hexagon whose sides have a length of 12 cm and whose apothem is 10.4 cm.

p = 6s

Formula for the perimeter of a hexagon

p = 6( 12 cm)

Substitute 12 cm for s

p = 72 cm

6 times 12

A = ap/2

Formula for finding the regular polygon

A = (10.4 cm(72 cm))/2

a = 10.4 and p = 72

A = 10.4 (36 cm²)

Divide 72 by 2

A = 367.4 cm²

10.4 times 36

Problems:

1) Find the area of a regular octagon whose sides have a length of 10 cm and whose apothem is 5 cm .

2) Find the area of a regular decagon whose sides have a length of 2 in and whose apothem is .7 in.