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Regular Polygon Area Calculator

Calculate the perimeter, apothem, and area of any regular polygon (pentagon, hexagon, octagon, etc.) from its number of sides and side length.

Polygon Area
166.277
Perimeter (n Γ— s)
48.00
Apothem (Inradius)
6.928
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Calculation Guide & Reference

Regular Polygon Area & Apothem Mathematics

Regular polygon calculator computes the perimeter, apothem, and area of any regular polygon from its number of sides and side length.

Standardized Mathematical Formula
Area = (1/2) Γ— Perimeter Γ— Apothem | Apothem = s / (2Β·tan(Ο€/n))

A regular polygon can be divided into n identical isosceles triangles meeting at the center. The apothem β€” the perpendicular distance from center to a side β€” acts like a triangle's height, so the whole polygon's area is half its perimeter times its apothem.

Variables:
n:Number of sides
s:Length of each side (all equal in a regular polygon)
Apothem:Perpendicular distance from center to a side
How It Works (Step-by-Step)
  • 1Enter the number of sides (n) and the length of each side (s).
  • 2View the perimeter, apothem, and total area.
Real-World Numerical Example
A Regular Hexagon with Side Length 4

A regular hexagon (6 sides) has a side length of 4 units.

β€’Perimeter: 6 Γ— 4 = 24 units.
β€’Apothem: 4 Γ· (2 Γ— tan(Ο€/6)) = 4 Γ· (2 Γ— 0.5774) β‰ˆ 3.464 units.
β€’Area: (1/2) Γ— 24 Γ— 3.464 β‰ˆ 41.57 square units.
Result: The hexagon has a perimeter of 24 units and an area of approximately 41.57 square units.
Calculation Best Practices & Tips
Examine the discriminant (bΒ² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

The apothem is the perpendicular distance from the center of a regular polygon to the midpoint of any one of its sides β€” it plays the same role as a triangle's height in the polygon's area formula.

No β€” this formula requires all sides and angles to be equal (a "regular" polygon). Irregular polygons need different methods, like dividing them into triangles or using the shoelace formula with vertex coordinates.

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