Area of a Hexagon Formula

Geometry Formulas: Area, Volume, Perimeter
Formula:

What is the formula for the area of a hexagon?

Answer

Area of a hexagon
A = (3√3 / 2) · a²

Here a is the side (or base). The result comes out in square units.

Where the formula comes from

A = (3√3 / 2) · a²

A regular hexagon is six identical equilateral triangles meeting at the centre. One such triangle of side a has area (√3/4)·a², and six of them give (3√3/2)·a² ≈ 2.598·a².

Worked examples

Let a = 4. Then the area of a hexagon ≈ 41.57 square units.

Let a = 2.5. Then the area of a hexagon ≈ 16.24 square units.

The common mistake

Using the distance across the hexagon as the side. The side is one edge; the width across the flats is a√3 and across the corners is 2a — three different numbers that are easy to swap.

Related Calculations

See Also

Geometry Formulas: Area, Volume, Perimeter

These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the area of a hexagon? (The answer is: A = (3√3 / 2) · a²). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter
Formula:

Values from the Formula

If a =Area
1≈ 2.6 square units
2≈ 10.39 square units
3≈ 23.38 square units
4≈ 41.57 square units
5≈ 64.95 square units
10≈ 259.81 square units

FAQ

What is the formula for the area of a hexagon?

Area of a hexagon A = (3√3 / 2) · a²

Where does this formula come from?

A regular hexagon is six identical equilateral triangles meeting at the centre. One such triangle of side a has area (√3/4)·a², and six of them give (3√3/2)·a² ≈ 2.598·a².

What is the most common mistake here?

Using the distance across the hexagon as the side. The side is one edge; the width across the flats is a√3 and across the corners is 2a — three different numbers that are easy to swap.

How do I use this formula?

Put your own numbers in place of the letters. With a = 2.5, for instance, the formula A = (3√3 / 2) · a² gives ≈ 16.24 square units.

See Also