Solutions to “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 meters. What is the area of the decagon?

p = 10s

p = 10(10 meters)

p = 100 meters

A = ap/2

A = ( 15.39 meters(100 meters))/2

A = 1539 meter²/2

A = 769.5 meters²

Problems:

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

p = 8s

p = 8(10 cm)

p = 80 cm

A = ap/2

A = ( 80 cm(5 cm))/2

A = 40(5) cm²

A = 200 cm²

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

p = 10s

p = 10(2 in)

p = 20 in

A = ap/2

A = ( .7 in(20 in))/2

A = (.7(10)) in²

A = 7 in²