Calculate the area, perimeter, and angles of any regular polygon by entering the number of sides and the side length.
Calculation Results
Polygon Type:–
Total Area:–
Perimeter:–
Interior Angle:–
Sum of Interior Angles:–
Apothem (Inradius):–
Understanding Regular Polygon Geometry
A regular polygon is a two-dimensional geometric shape where all sides have the same length and all interior angles are equal. Examples include equilateral triangles, squares, regular pentagons, and hexagons. Calculating the area of these shapes is a fundamental task in geometry, architecture, and engineering.
The Regular Polygon Area Formula
To find the area of a regular polygon with n sides and side length s, we use the following mathematical formula:
Area = (n × s²) / (4 × tan(π / n))
Where:
n is the number of sides.
s is the length of a single side.
tan is the tangent function.
π (Pi) is approximately 3.14159.
Key Components of a Polygon
Beyond the area, several other metrics define a polygon's properties:
Perimeter: The total length of the boundary, calculated as n × s.
Interior Angle: The angle between two adjacent sides, calculated as ((n – 2) × 180°) / n.
Apothem: The distance from the center of the polygon to the midpoint of any side. It acts as the "inradius" of the shape.
Sum of Interior Angles: The total degrees of all interior angles combined, which is (n – 2) × 180°.
Step-by-Step Calculation Example
Let's calculate the area of a Regular Hexagon (6 sides) with a side length of 8 units.