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