What is a Regular Hexagon? (Definition & Examples) - BYJUS

# Regular Hexagon

A regular hexagon is a closed two-dimensional shape made up of six straight lines. A regular hexagon has six sides, six vertices, and six interior angles in two dimensions. The name ‘hexagon’ is made up of the words 'hex' and 'gonia', which mean six and corners, respectively. Let us take a closer look at the regular hexagon shape in this article....Read MoreRead Less

## What are Regular Polygons?

Polygons that are equiangular and equilateral are regular polygons. Here is a list of regular polygons:

 Number of sides Name Figure 3 Equilateral triangle 4 Square 5 Regular Pentagon 6 Regular Hexagon

## What is a Regular Hexagon?

A closed-shape polygon with six equal sides and six equal angles is called a regular hexagon.

## Properties of a Regular Hexagon

• It has 6 sides of the same size and 6 angles of equal measure.

• It has a total of six vertices.

• The measure of each interior angle is 120° and the measure of each exterior angle is 60°.

• The angle sum of all the interior angles of a hexagon is 720°. The formula for finding the angle sum of a polygon is:

= (n – 2) x 180°, where n is the number of sides of a polygon.

• A regular hexagon can be divided into 6 equilateral triangles.

• The number of diagonals in a hexagon is 9. This can be found using the formula:

$$n~\times~\frac{(n-3)}{2}$$, where n is the number of sides of a polygon

• The opposite sides of a regular hexagon are parallel to each other.

## The Area and Perimeter of a Regular Hexagon

Now that we have discussed the definition and properties of a regular hexagon, let us look at its area and perimeter.

The area of a regular hexagon is calculated as follows:

$$A=\frac{3\sqrt 3}{2}~\times~a^2$$

or,

$$A=2.59807a^2$$

Where a is the length of one of its sides.

The perimeter of the hexagon is:

P = 6a

Where a denotes the length of a side.

## The Angles of a Regular Hexagon

The sum of the angles of a regular hexagon with all six sides equal is 720°, as we already know.

As a result, the interior and exterior angles are as follows:

Each interior angle is equal to

$$\frac{720^{\circ}}{6}=120^{\circ}$$

Each exterior angle = 180° – interior angle

= 180° – 120°

= 60°

## Solved Regular Hexagon Examples

Example 1:

What is the area of a regular hexagon that has a side of 3 units?

Solution:
As we know, the area of a regular hexagon $$A=\frac{3\sqrt 3}{2}~\times~a^2$$ square units.

Given, the side of a regular hexagon ‘a= 3 units.

Therefore, the area is:

$$A=\frac{3\sqrt 3}{2}~\times~3^2$$

$$=\frac{3\sqrt 3}{2}~\times~9$$

$$=\frac{27\sqrt 3}{2}$$         Substitue $$\sqrt 3=1.732$$ and simplify.

= 23.38 square units

As a result, the required area is 23.38 square units.

Example 2:

Calculate the perimeter of a regular hexagon with 30 cm long sides.

Solution:

It is given that the side of a regular hexagon ‘a=30 cm.

The perimeter of a regular hexagon = 6 x a

= 6 × 30 cm

= 180 cm

As a result, the perimeter of the hexagon is 180 cm.

Example 3:

If the perimeter of a regular hexagon is 108 units, what is the length of each side?

Solution:
The perimeter of the regular hexagon = 108 units.

The length of the sides can be calculated as

$$\frac{Perimeter}{6}$$

= $$\frac{108}{6}$$

= 18 units

As a result, each side of the hexagon measures 18 units in length.

Frequently Asked Questions on Regular Hexagon

Hexagons have six sides, six angles, and six vertices.

There are 9 diagonals in a hexagon.

The sum of the interior angles of a hexagon is $$720^{\circ}$$.

A hexagon, if not regular, does not have all sides of equal length. All sides of a regular hexagon are of the same length.

Hexagons can be classified as:

• Regular Hexagon
• Irregular Hexagon
• Concave Hexagon
• Convex Hexagon

The measure of all the interior angles of a concave polygon is less than 180 degrees. In contrast, a concave polygon has at least one interior angle having a measure of more than 180 degrees.