Regular Polygon Area Calculator

Calculate the area of any regular polygon quickly and easily. Just enter the side length and the number of sides.

Side Length:

Number of Sides:

Polygon Visualization

Result:

Area:

Understanding Regular Polygon Area

A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). To calculate the area of a regular polygon, we use the formula:

$$Area = \frac {1} {2} * p * a$$

Where:

p is the perimeter of the polygon (Perimeter = number of sides × side length).
a is the apothem (the perpendicular distance from the center to a side).

Alternatively, the area can also be calculated using the side length (s) and number of sides (n) with the formula:

$$Area = \frac {1} {4} * n * s^2 * cot(\frac{\pi}{n})$$

This calculator simplifies this process, allowing you to quickly find the area by just inputting the side length and the number of sides. It's useful for educational purposes, geometry problems, and various design and construction tasks.

For further reading, you can refer to resources like Wikipedia on Regular Polygons or educational math websites.