top of page
Circumference, Area,
Surface Area, and Volume
By Taylor Winter
Derive the Formula:
Area of a Regular Polygon
Example Problems
1. A hexagon has a side length of 6 cm and an apothem of 3 cm. What is the area?
Area of a regular polygon= 1/2p x a
p= 6 cm x 6 sides = 36cm a= 3 cm
(1/2 x 36 cm) x 3 cm
18 cm x 3 cm = 54 cm^2
The area of the hexagon is 54 cm^2.
Since it is a regular polygon it can be broken up into equilateral triangles using the additive and moving principles. These triangles can be arranged into a parallelogram.
Then using the area of a parallelogram do base x height.
Base is equal to half of the perimeter since it is half of the sides of the original polygon.
Height is equal to the apothem of the regular triangle.
The area of a regular polygon is 1/2 perimeter x the apothem.
2. A pentagon has a side length of 7 ft and an apothem of 4 ft. What is the area?
Area of a regular polygon= 1/2p x a
p= 7 ft x 5 sides = 35 ft a= 4 ft
(1/2 x 35 ft) x 4 ft
17.5 ft x 4 ft = 70 ft^2
The area of the pentagon is 70 ft^2.
bottom of page