GeomBench

Regular Polygon Area Calculator

Works for any number of sides, from triangles to 20-gons.

Number of sides

Side length

Area

64.952

Perimeter: 30

What you entered

Sides: 6Side length: 5

1
Perimeter
6 × 5= 30
2
Area = (n × s²) ÷ (4 × tan(π/n))
(6 × 5²) ÷ (4 × tan(π/6))= 64.9519

Result

Area: 64.952

A regular 6-sided polygon with side length 5 has an area of 64.952 and a perimeter of 30.

Regular polygon area at a fixed side length of 5

Each row is a regular polygon with every side 5 units, showing how area grows with the number of sides.

Sides	Shape	Perimeter	Area
3	Triangle	15.00	10.8253
4	Square	20.00	25.0000
5	Pentagon	25.00	43.0119
6	Hexagon	30.00	64.9519
8	Octagon	40.00	120.7107
12	Dodecagon	60.00	279.9038

Adding sides at a fixed side length grows both perimeter and area, but area far faster - doubling the sides from 6 to 12 doubles the perimeter and more than quadruples the area. A different and more famous question is what happens at fixed perimeter: there the polygon with more sides always encloses more area, and the limit as sides go to infinity is the circle, which encloses the most area for any given perimeter. The square row is the useful sanity check, since 5 squared is exactly 25.

One formula for every regular shape

Every regular polygon can be split into n identical isosceles triangles meeting at the center. Summing their areas gives A = (n × s²) ÷ (4 × tan(π/n)) — valid for a triangle, hexagon, or any n-gon.

As n grows, it approaches a circle

The more sides a regular polygon has, the closer its area gets to that of its circumscribed circle — a hexagon is already a decent approximation, and a 20-gon is nearly indistinguishable from round.

Frequently asked questions

How do I calculate the area of a regular polygon?

Area = (n × s²) / (4 × tan(π/n)), where n is the number of sides and s is the side length. Or Area = ½ × perimeter × apothem. For a regular hexagon with side 10: Area = (6 × 100) / (4 × tan(30°)) = 600 / 2.309 = 259.8.

What is a regular polygon?

A regular polygon has all sides equal and all interior angles equal. Examples: equilateral triangle (3), square (4), regular pentagon (5), regular hexagon (6). An irregular polygon has sides or angles that differ.

What is the interior angle of a regular polygon?

Interior angle = (n−2) × 180° / n. Triangle: 60°, square: 90°, pentagon: 108°, hexagon: 120°, octagon: 135°. As n increases, the angle approaches 180° (and the polygon approaches a circle).