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