Pentagon
\(n = 5, s = 6 \rightarrow A = 61.94\) sq units
Polygon Calculator
Calculate regular polygon area, perimeter, and interior angles
Results
Enter values and click Calculate to see the result.
Theory & Formula
A regular polygon is a polygon with all sides equal in length and all interior angles equal. It can be inscribed in a circle (circumscribed) and has a circle inscribed within it.
Key formulas for a regular n-sided polygon with side length s:
- Perimeter: Perimeter: P = n × s
- Apothem: Apothem: a = s / (2 × tan(π/n))
- Area: Area: A = (n × s × a) / 2 or A = (n × s²) / (4 × tan(π/n))
- Circumradius: Circumradius: R = s / (2 × sin(π/n))
- Interior angle: Interior angle: ((n - 2) × 180°) / n
- Exterior angle: Exterior angle: 360° / n
\(A = \frac{n \times s \times a}{2}\)
Worked Examples
Hexagon
\(n = 6, s = 4 \rightarrow A = 41.57\) sq units