Regular Hexagon — Definition, Formula & Examples

A regular hexagon is a polygon with six sides that are all the same length and six angles that are all equal (each measuring 120°).

A regular hexagon is an equilateral and equiangular polygon with six sides, where each interior angle measures exactly 120° and the sum of all interior angles is 720°.

Key Formula

A = \frac{3\sqrt{3}}{2}\,s^2

Where:

$A$ = Area of the regular hexagon
$s$ = Length of one side

How It Works

A regular hexagon can be divided into six equilateral triangles by drawing lines from the center to each vertex. This is why the distance from the center to any vertex equals the side length. The apothem (distance from the center to the midpoint of a side) is used in the area formula. You can find the area either by using the apothem or by using only the side length.

Worked Example

Problem: Find the area and perimeter of a regular hexagon with a side length of 6 cm.

Perimeter: Multiply the side length by 6.

P = 6s = 6 \times 6 = 36 \text{ cm}

Area formula: Substitute s = 6 into the area formula.

A = \frac{3\sqrt{3}}{2}(6)^2 = \frac{3\sqrt{3}}{2} \times 36 = 54\sqrt{3}

Approximate: Use √3 ≈ 1.732 to get a decimal value.

A \approx 54 \times 1.732 \approx 93.5 \text{ cm}^2

Answer: The perimeter is 36 cm and the area is

54\sqrt{3} \approx 93.5

cm².

Why It Matters

Regular hexagons tile a flat surface with no gaps, which is why you see them in honeycombs, floor tiles, and bolt heads. Understanding their geometry also prepares you for coordinate geometry and trigonometry problems in high school.

Common Mistakes

Mistake: Confusing the apothem with the side length or the radius (center-to-vertex distance).

Correction: The radius of a regular hexagon equals the side length s, but the apothem is shorter:

a = \frac{s\sqrt{3}}{2}

. Make sure you identify which measurement a problem gives you before plugging into a formula.