Area of a Regular polygon Calculator
A regular polygon splits into n identical triangles meeting at the center. Each has base s and height equal to the apothem. For a hexagon (n = 6) this simplifies to A = (3√3 / 2) s².
A = n × s² / (4 × tan(π/n))
Perimeter: P = n × s
Area of the regular polygon
41.5692ft²
- Perimeter
- 24 ft
- Apothem = s / (2 tan(π/n)) = 3.4641 ft
- A = ½ × perimeter × apothem = 41.5692 ft²
Area in other units
| m² | 3.8619 |
| cm² | 38,619.1 |
| ft² | 41.5692 |
| in² | 5,985.97 |
| yd² | 4.6188 |
| acres | 0.000954 |
| hectares | 0.000386 |
How to find the area of a regular polygon
Formula: A = n × s² / (4 × tan(π/n)). Perimeter: P = n × s.
- Measure every length in the same unit. Mixing feet and inches is the most common mistake; convert first (6 in = 0.5 ft).
- Put the numbers into the formula above. The calculator shows each substitution with your numbers.
- Area comes out in square units (ft², m²). If you need a different unit, open "Area in other units".
Questions people ask
What is the area of a regular hexagon?
A = (3√3/2) × s² ≈ 2.598 × s². A hexagon with 4 cm sides is about 41.57 cm².
What about an irregular polygon?
Split it into triangles and add them, or use the shoelace formula on the corner coordinates.
Stuck on a word problem?
Paste a homework question or describe your project. The AI tutor names the formula and works it through step by step. Always check the result with the calculator above.
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