Area of a Regular Polygon Calculator
The area of a regular polygon is n s² ÷ (4 tan(π/n)): a regular hexagon with 4 cm sides has an area of 41.5692 cm².
41.5692193816531 cm²
Full answer, then cut to fewer decimals (not rounded):
- 41.5692193816531 cm²
- 41.569219381653 cm²
- 41.56921938165 cm²
- 41.5692193816 cm²
- 41.569219381 cm²
- 41.56921938 cm²
- 41.5692193 cm²
- 41.569219 cm²
- 41.56921 cm²
- 41.5692 cm²
- 41.569 cm²
- 41.56 cm²
- 41.5 cm²
- Area
- 41.5692 cm²
- Apothem
- 3.4641 cm
- Perimeter
- 24 cm
- Interior angle
- 120°
In other units: 0.00415692 m² · 4156.92 mm² · 4.15692 × 10⁻⁹ km² · 4.15692 × 10⁻⁷ ha · 0.0447447 ft² · 6.44324 in² · 0.00497164 yd² · 0.0000010272 ac · 1.605 × 10⁻⁹ mi²
Step-by-step solution
- A = n s² ÷ (4 tan(π ÷ n))
- A = 6 × 4² ÷ (4 × tan(180° ÷ 6)) = 41.5692 cm²
Area of a Regular Polygon Formula
A = n s² ÷ (4 tan(π ÷ n))
n number of sides, s side length
Worked Example
A regular hexagon with 4 cm sides:
- A = n s² ÷ (4 tan(π ÷ n))
- A = 6 × 4² ÷ (4 × tan(180° ÷ 6)) = 41.5692 cm²
Apothem: 3.4641 cm · Perimeter: 24 cm · Interior angle: 120°
Same area in other units: 0.00415692 m² · 4156.92 mm² · 4.15692 × 10⁻⁹ km² · 4.15692 × 10⁻⁷ ha · 0.0447447 ft²
Frequently asked questions
What is the formula for the area of a hexagon?
For a regular hexagon, A = (3√3 ÷ 2) s² ≈ 2.598 s². A 6 cm side gives 93.53 cm².
How do I find the area using the apothem?
A = ½ × perimeter × apothem, where the apothem is the distance from the centre to the middle of a side. It gives the same result as the n s² formula.
What are the area formulas for a pentagon and an octagon?
Pentagon: A ≈ 1.7205 s². Octagon: A = 2(1 + √2) s² ≈ 4.8284 s².
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 2008 Edition, National Institute of Standards and Technology .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Area of a Regular Polygon Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/area-of-a-regular-polygon/
IEEE
Scientific Converters, "Area of a Regular Polygon Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/area-of-a-regular-polygon/