# Hexagon – Definition, Types, Properties, Examples, FAQs

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## What is a Hexagon?

In geometry, a hexagon can be defined as a closed two-dimensional polygon with six sides.

Hexagon has 6 vertices and 6 angles also.

Hexa means six and gonia means angles.

Hexagon in Real Life

We can find the shape of a hexagon in a honeycomb, a football, face of pencil, and floor tiles.

## Types of Hexagons

Hexagonal shape is classified into several types based on the measure of sides and angles.

Classification of hexagons based on their sides

### 1. Regular Hexagon

When the length of all the sides and measure of all the angles are equal, it is a regular hexagon. All interior angles of a regular hexagon are 120 degrees each.

### Properties of a Regular Hexagon

• All the sides are equal in length.
• All the interior angles measure 120°.
• All the exterior angles measure 60°.
• Since all angles are equal in a regular hexagon, each angle is 120o and the sum of all the interior angles is 720o
• A regular hexagon can be divided into six equilateral triangles.
• The opposite sides of a regular hexagon are parallel to each other.
• A regular hexagon is also a convex hexagon.

### Symmetry in regular hexagon:

A regular hexagon has 6 lines of symmetry and a rotational symmetry of order 6

### 2. Irregular Hexagon

In an irregular hexagon, the length of sides and measure of angles do not have the same measure.

## Classification of hexagons based on their angles

### 1. Convex Hexagon

For convex hexagons, all of its interior angles must be less than 180 degrees, and all the vertices are pointed outwards. Convex hexagons can be regular or irregular.

### 2. Concave Hexagon

For concave hexagons, at least one of its interior angles must be greater than 180° and at least one of its vertex points inwards.

### Properties of Hexagon

• It is two-dimensional.
• It has six sides, six edges and six vertices.
• The sum of the interior angles is 720 degrees.
• It has nine diagonals.

## Perimeter of a Hexagon

The perimeter of a hexagon is the sum of the length of all 6 sides.

Perimeter = AB + BC + CD + DE + EF + FA

In regular hexagons, all sides are equal in length. So, the perimeter of a regular hexagon is six times the length of one side.

Perimeter = a + a + a + a + a + a = 6a

## Solved Examples on Hexagon

Example 1: Find the perimeter of a regular hexagon having each side measure 20 cm.

Solution:

Perimeter of regular hexagon = 6 × length of side

= 6 × 20 cm

= 120 cm

So, the perimeter of the hexagon is 120 cm.

Example 2: The perimeter of a regular hexagon is 36 cm. What is the length of its sides?

Solution:

Perimeter of regular hexagon = 6 × length of side

36 = 6 × length of side

Length of side = 366 cm = 6 cm

So, the length of its sides is 6 cm.

Example 3: Five angles of a hexagon measure 110° each. What is the measure of the sixth angle?

Solution:

Sum of the interior angles in hexagon = 720°

Sum of five angles = 5 × 110° = 550°

Sixth angle = 720° – 550° = 170°

So, the measure of the sixth angle is 170°.

## Practice Problems On Hexagon

1

### What is the measure of each interior angle of a regular hexagon?

60°
100°
120°
720°
CorrectIncorrect
The sum of the interior angles of a hexagon is 720° For a regular hexagon all the sides are of the same length and all interior angles are equal. So, each interior angle= 720/6 = 120° So, the measure of the interior angle of a regular hexagon is 120°.
2

### A plane with six sides is classified as

pentagon
hexagon
heptagon
octagon
CorrectIncorrect
Hexagon is a two dimensional polygon with six sides.
3

### The hexagon is said to be convex hexagon if none of its interior angles is

90°
less than 90°
more than 90° and less than 180°
more than 180°
CorrectIncorrect
Correct answer is: more than 180°
more than 180° For convex hexagons, all of its interior angles must be less than 180 degrees. For concave hexagons, at least one of its interior angles must be greater than 180°.
4

### A regular hexagon has how many lines of symmetry

4
6
8
9
CorrectIncorrect
A regular hexagon has 6 lines of symmetry. In a regular polygon the lines of symmetry are equal to the number of sides. So there will be 6 lines of symmetry for a regular hexagon.

## Frequently Asked Questions On Hexagon

There are four types of hexagons. These are regular hexagons, irregular hexagons, concave hexagons, and concave hexagons.

Hexagon has 6 sides, 6 angles and 6 vertices.

The sum of all interior angles of a hexagon is 720°.

A hexagon has 9 diagonals.

No, hexagons can have sides with different lengths. Regular hexagon has all sides are equal in length.

Yes, all six sided shapes are called hexagons.