Polygon Calculator
Calculate area, perimeter, and properties of regular polygons.
Area
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Enter parameters
Perimeter
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Apothem
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Interior Angle
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Exterior Angle
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Circumradius
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Sum of Angles
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Diagonals
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Name
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Regular Polygons
A regular polygon has all sides equal and all angles equal.
Formulas
Area = (n × s² × cot(π/n)) / 4
Perimeter = n × s
Apothem = s / (2 × tan(π/n))
Perimeter = n × s
Apothem = s / (2 × tan(π/n))
Polygon Properties
| n | Name | Interior Angle | Diagonals |
|---|---|---|---|
| 3 | Triangle | 60° | 0 |
| 4 | Square | 90° | 2 |
| 5 | Pentagon | 108° | 5 |
| 6 | Hexagon | 120° | 9 |
| 8 | Octagon | 135° | 20 |
| 10 | Decagon | 144° | 35 |
Key Relationships
- Sum of Interior Angles: (n-2) × 180°
- Each Interior Angle: (n-2) × 180° / n
- Exterior Angle: 360° / n
- Number of Diagonals: n(n-3)/2
Frequently Asked Questions
What is the apothem?
The apothem is the distance from the center to the midpoint of any side. It's like the "radius" of the inscribed circle.
How is circumradius different from apothem?
Circumradius (R) is from center to a vertex, apothem (r) is from center to midpoint of a side. R > r for any polygon with n > 3.