Area of a Regular Polygon Calculator
A = ¼ × n × s² × cot(π/n) for an n-gon with side length s.
Result
Area
64.9519 units²
Apothem: 4.3301, perimeter: 30.0000.
- Sides6
- Side length5
- Apothem (in-radius)4.3301
- Circum-radius5.0000
- Perimeter30.0000
- Interior angle120.00°
Step-by-step
- cot(π/6) = 1/tan(30.00°) = 1.7321.
- Area = ¼ × 6 × 5² × 1.7321 = 64.9519.
- Equivalent: ½ × perimeter × apothem = ½ × 30.00 × 4.33.
How to use this calculator
- Enter the number of sides (3 or more).
- Enter the side length.
- Read area, apothem, circum-radius, and perimeter.
About this calculator
A regular polygon has equal-length sides and equal interior angles. The classic formula A = ¼ n s² cot(π/n) collapses to familiar special cases — equilateral triangle (n=3): √3/4 s²; square (n=4): s²; regular hexagon (n=6): 3√3/2 s². The "apothem" is the distance from center to side midpoint.
Frequently asked
The perpendicular distance from the polygon's center to the midpoint of any side. Also the in-circle radius.
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