Regular Polygon Area
Calculator
Results
- Area
- 64.951905
- Perimeter
- 30
- Apothem
- 4.330127
- Interior angle (degrees)
- 120
Results
| Area | 64.951905 |
| Perimeter | 30 |
| Apothem | 4.330127 |
| Interior angle (degrees) | 120 |
formula-map diagram
- Area
- 64.951905
- Perimeter
- 30
- Apothem
- 4.330127
- Interior angle (degrees)
- 120
Formula map
Formula
A = (n × s²) ÷ (4 × tan(π ÷ n))= 64.951905283833
Note
Simplified model: these are exact results of the stated idealised formulas, assuming perfect shapes and exact inputs. Real measurements carry error, and the ellipse perimeter is a Ramanujan approximation. Verify independently before relying on these figures.
More in Mathematics
See all →Frequently asked questions
What do I need to know about the polygon?+
The number of sides (n) and either the side length or the apothem (the distance from the center to the middle of a side), depending on which the calculator asks for.
How does the formula work?+
A regular polygon can be split into n identical triangles from the center. The area is (1/2) × perimeter × apothem, or equivalently a formula in terms of side length and number of sides using trigonometry.
What's the difference between the apothem and the radius (circumradius)?+
The apothem is the distance from the center to the midpoint of a side, while the circumradius is the distance from the center to a vertex (corner). The circumradius is always longer than the apothem for the same polygon.
Does this work for irregular polygons?+
No, this formula only applies to regular polygons, where all sides and all interior angles are equal. An irregular polygon needs a different method, such as breaking it into triangles or using coordinates.
Why does the polygon's area approach a circle's area as sides increase?+
As the number of sides grows, a regular polygon looks more and more like a circle, and its area formula mathematically converges toward πr² in the limit of infinite sides.