Hexagon – Definition with Examples

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.

Examples

Non – Examples

Hexagon in Real Life

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

Hexagon around us

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 120^o and the sum of all the interior angles is 720^o. 

• 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

6 lines of symmetry

Six 60° angles of rotation

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

Frequently Asked Questions