Regular Hexagon Formulas
Perimeter = 6 × s
Apothem (inradius) = (√3 / 2) × s ≈ 0.866 × s
Circumradius = s
Long diagonal = 2 × s
Short diagonal = √3 × s ≈ 1.732 × s
Where s is the side length of the regular hexagon. In a regular hexagon, the circumradius (center to vertex) equals the side length.
Example
Regular hexagon with side = 6 cm
Area = (3√3/2) × 36 = 93.53 cm²
Perimeter = 6 × 6 = 36 cm
Apothem = (√3/2) × 6 = 5.196 cm
Long diagonal = 2 × 6 = 12 cm
Properties of a Regular Hexagon
- 6 equal sides, 6 equal interior angles of 120° each
- Can be divided into 6 equilateral triangles
- The circumradius equals the side length — unique among regular polygons
- Appears in nature: honeycomb cells, snowflake structure, basalt columns
- Highest area-to-perimeter ratio among regular polygons that tile a plane
Frequently Asked Questions
What is an apothem?
The apothem is the perpendicular distance from the center of the hexagon to the midpoint of any side. It is also the inradius — the radius of the largest circle that fits inside the hexagon. For a regular hexagon: apothem = (√3/2) × side.
Why do bees use hexagons for honeycomb?
Regular hexagons pack together perfectly with no gaps (tessellate) and use the minimum amount of wax for the maximum storage area — the most efficient shape that tiles a plane. Circles would waste space at the gaps; squares and triangles use more material for the same area.
What is the difference between the two diagonals?
A regular hexagon has two types of diagonal: the long diagonal passes through the center connecting opposite vertices (= 2 × side); the short diagonal connects vertices separated by one vertex (= √3 × side ≈ 1.732 × side).