Area of Regular Pentagon
The area of a regular pentagon can be calculated if only the side length 's' is known. The formula used to find the area of a regular pentagon,
84.3 square units.
Area of Pentagon with Apothem
The area of a pentagon can be calculated if the side and apothem is given. The formula that is commonly used to find the area of any regular polygon using the apothem and side is, Area of regular polygon = 1/2 × perimeter of polygon × apothem.
So, Area of regular pentagon = 1/2 × p × a; where 'p' is the perimeter of the pentagon and 'a' is the apothem of the pentagon. Let us understand this with an example.
Example: Find the area of a regular pentagon whose side length is 18 units and the length of apothem is 5 units.
Solution: Given that side length 's' = 18 units and apothem 'a' = 5 units, let us first find the perimeter of the pentagon. Perimeter of pentagon = 5 × side length = 5 × 18 = 90 units. Now, let us substitute these values in the formula
Area of the pentagon, A = 1/2 × p × a; where p = 90, a = 5
⇒ A = 1/2 × 90 × 5
⇒ A = 225 square units
Therefore, the area of the pentagon is 225 square units.
