Regular Polygon Area Calculator – ProMathTools

Regular Polygon Area

This calculator helps you find the area of any regular polygon. Just enter the number of sides and the length of one side, and we'll do the math for you. A regular polygon is a shape where all sides are equal in length and all interior angles are equal.

Number of Sides (n)

Enter an integer greater than or equal to 3.

Side Length (s)

Enter a positive value for the length of one side.

Please enter a valid number of sides (at least 3).

How it works

This calculator helps you find the area of any regular polygon. Just enter the number of sides and the length of one side, and we'll do the math for you. A regular polygon is a shape where all sides are equal in length and all interior angles are equal.

The Formula

Area = (n × s²) / (4 × tan(π/n)) Where:
n = Number of sides
s = Length of one side
π = Pi (approximately 3.14159)

Worked Example

Example: Area of a Regular Hexagon
Imagine you have a regular hexagon (6 sides) where each side measures 5 units. To find its area, you would input '6' for the number of sides and '5' for the side length. The calculator applies the formula: Area = (6 × 5²) / (4 × tan(π/6)). The result would be approximately 64.95 square units.

Tips, Assumptions & Limitations

Ensure your side length is in consistent units (e.g., all in cm or all in inches). The area will be in square units of your input.
A regular polygon must have at least 3 sides (a triangle).
The formula relies on trigonometry, specifically the tangent function, to account for the polygon's internal angles.

FAQ

A regular polygon is a two-dimensional shape where all its sides are equal in length, and all its interior angles are equal in measure. Examples include equilateral triangles, squares, regular pentagons, and hexagons.

Simply enter the number of sides your regular polygon has (e.g., 3 for a triangle, 4 for a square, 5 for a pentagon) into the 'Number of Sides' field. Then, input the length of one of its sides into the 'Side Length' field. Click 'Calculate' to see the area.

No, this calculator is specifically designed for regular polygons. Irregular polygons have sides of different lengths or angles of different measures, requiring more complex methods like dividing the polygon into simpler shapes (triangles) or using coordinate geometry.