Regular Polygon Area Calculator
Compute the area, perimeter, and interior angles of any regular polygon from its side count and side length — triangle to megagon.
Area (unit²)
61.94
Breakdown
- Perimeter
- 30
- Apothem (inradius)
- 4.13
- Circumradius
- 5.10
- Interior angle (°)
- 108
- Exterior angle (°)
- 72
- Area in acres (if feet)
- 0
- Unit
- cm
Last updated:
FAQ
What is the formula for a regular polygon's area?
A = n × s² / (4 × tan(π/n)), where n is the side count and s the side length. It comes from slicing the polygon into n identical triangles from the center — each with base s and height equal to the apothem.
What is the apothem?
The apothem is the distance from the center to the midpoint of a side — the height of each triangle slice, and the radius of the inscribed circle. Carpenters know it as the width of board needed to cut each side flat.
Why does a polygon with more sides approach a circle?
As n grows, the perimeter stays n×s while the area approaches that of a circle with circumference n×s. At n = 96, the polygon is already within 0.02% of the circle — the same insight Archimedes used to bound π.
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