Regular Polygon Area Calculator Formula
Understand the math behind the regular polygon area calculator. Each variable explained with a worked example.
Formulas Used
Area
area = (n * pow(side_len, 2)) / (4 * tan(pi / n))Perimeter
perimeter = n * side_lenInterior Angle
interior_angle = (n - 2) * 180 / nApothem
apothem = side_len / (2 * tan(pi / n))Variables
| Variable | Description | Default |
|---|---|---|
n | Number of Sides | 6 |
side_len | Side Length | 5 |
How It Works
Regular Polygon Formulas
Area
Area = (n × s²) / (4 × tan(pi/n))
Alternatively: Area = (1/2) × perimeter × apothem
Interior Angle
Interior angle = (n - 2) × 180 / n degrees
Apothem
Apothem = s / (2 × tan(pi/n))
The apothem is the distance from the center to the midpoint of a side.
Worked Example
Regular hexagon with side length 5.
- 01Area = (6 × 25) / (4 × tan(pi/6)) = 150 / (4 × 0.5774) ≈ 64.9519
- 02Perimeter = 6 × 5 = 30
- 03Interior angle = (6-2) × 180/6 = 120°
- 04Apothem = 5 / (2 × 0.5774) ≈ 4.3301
Frequently Asked Questions
What is a regular polygon?
A regular polygon has all sides equal in length and all interior angles equal. Examples include equilateral triangles, squares, pentagons, and hexagons.
What is the apothem?
The apothem is the distance from the center of the polygon to the midpoint of any side. It is also the radius of the inscribed circle.
How does the interior angle change with more sides?
As the number of sides increases, the interior angle approaches 180 degrees. A triangle has 60°, a square 90°, a pentagon 108°, a hexagon 120°, etc.
Ready to run the numbers?
Open Regular Polygon Area Calculator