Hexagon

A hexagon is a six-sided polygon. A regular hexagon has all sides equal and all interior angles equal to 120°.

r a 120°

Properties of Regular Hexagon

A regular hexagon can be divided into 6 equilateral triangles. Its circumradius equals its side length: R = a. This makes hexagons particularly efficient for tiling (honeycombs).

Basic Formulas

S = (3√3/2) · a² Area of regular hexagon
P = 6a Perimeter (six times side length)
r = (√3/2) · a Apothem (inradius — distance from center to side)
R = a Circumradius equals side length
α = 120° Each interior angle

Example

Given: side a = 6 cm

Area: S = (3√3/2) · 6² = (3√3/2) · 36 = 54√3 ≈ 93.531 cm²

Perimeter: P = 6 · 6 = 36 cm

Apothem: r = (√3/2) · 6 = 3√3 ≈ 5.196 cm

Circumradius: R = 6 cm

Notes

The regular hexagon is one of only three regular polygons that can tile the plane without gaps (along with triangles and squares). This is why honeycombs use hexagonal cells — they provide maximum storage area with minimal material.

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