What is the Formula for the Area of an n-sided Regular Polygon?

Are you looking for the formula for the area of an n-sided regular polygon? If so, you are in luck, as there is a simple formula to calculate the area of any n-sided regular polygon.

What is a Regular Polygon?

Before we get into the formula for the area of an n-sided regular polygon, let's first define what a regular polygon is. A regular polygon is a closed two-dimensional shape with straight sides and all angles are equal. The most common type of regular polygon is a triangle, which has three sides, followed by a square, which has four sides. Polygons with more than four sides are often referred to as pentagons, hexagons, heptagons, octagons, and so on.

The Formula for the Area of an n-sided Regular Polygon

The formula for the area of an n-sided regular polygon is as follows:

Area = (n × s²) ÷ (4 × tan(π ÷ n))

Where:

n = number of sides

s = length of one side

π = 3.14159

Example

Let's say you want to calculate the area of a regular pentagon with a side length of 7 units. Using the formula above, the area would be calculated as follows:

Area = (5 × 7²) ÷ (4 × tan(π ÷ 5)) = 61.731

Therefore, the area of the pentagon is 61.731 square units.