Overview
A regular polygon has equal sides and equal angles, such as an equilateral triangle, a square or a regular pentagon. It can be divided into congruent triangles from its center, which makes its area easy to compute.
Formula
Perimeter = n × s, area = (n × s × a) ÷ 2, where a is the apothem.
How it works
Enter the number of sides
A whole number of at least 3.
Enter the side length
All sides are equal in a regular polygon.
Compute the perimeter
Multiply the number of sides by the side length.
Compute area and angles
Use the apothem and the interior and exterior angles.
Worked examples
Example 1: regular hexagon with side 4
Perimeter 24, apothem ≈ 3.4641, area ≈ 41.5692, interior angle 120°.
Example 2: square with side 5
Perimeter 20, apothem 2.5, area 25, interior angle 90°.
Frequently asked questions
What is the apothem?
The perpendicular distance from the center of a regular polygon to the midpoint of a side.
What is the sum of interior angles?
The sum = (n − 2) × 180 degrees.
Can I compute the area without the apothem?
Yes, using a formula based directly on the side length and number of sides.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.