Regular Polygon Calculator
A regular polygon has all sides equal and all interior angles equal. As the number of sides increases, it approaches a circle. Regular polygons are used in architecture, design, and tessellations.
- 1Sum of interior angles = (n−2) × 180°
- 2Each interior angle = (n−2) × 180° / n
- 3Area = (n × s²) / (4 × tan(π/n))
- 4Apothem (inradius) = s / (2 × tan(π/n))
| Polygon | Sides | Interior angle | Sum of angles |
|---|---|---|---|
| Triangle | 3 | 60° | 180° |
| Square | 4 | 90° | 360° |
| Pentagon | 5 | 108° | 540° |
| Hexagon | 6 | 120° | 720° |
| Octagon | 8 | 135° | 1,080° |
| Decagon | 10 | 144° | 1,440° |
| Dodecagon | 12 | 150° | 1,800° |
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Fun Fact
Honeycombs use regular hexagons because they tile the plane perfectly and use the least wax for the most storage area — a property mathematically proven in 1999.
References
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