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

s = 4n = 6
Area of the regular polygon
41.5692ft²
Perimeter
24 ft
  1. Apothem = s / (2 tan(π/n)) = 3.4641 ft
  2. A = ½ × perimeter × apothem = 41.5692 ft²
Area in other units
m²3.8619
cm²38,619.1
ft²41.5692
in²5,985.97
yd²4.6188
acres0.000954
hectares0.000386

How to find the area of a regular polygon

Formula: A = n × s² / (4 × tan(π/n)). Perimeter: P = n × s.

  1. Measure every length in the same unit. Mixing feet and inches is the most common mistake; convert first (6 in = 0.5 ft).
  2. Put the numbers into the formula above. The calculator shows each substitution with your numbers.
  3. 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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