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 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
| 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 On Hexagon
Hexagon
What is the measure of each interior angle of a regular hexagon?
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°.
A plane with six sides is classified as
Hexagon is a two dimensional polygon with six sides.
The hexagon is said to be convex hexagon if none of its interior angles is
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°.
A regular hexagon has how many lines of symmetry
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
How many types of hexagons are there?
There are four types of hexagons. These are regular hexagons, irregular hexagons, concave hexagons, and concave hexagons.
What are the three characteristics of a hexagon?
Hexagon has 6 sides, 6 angles and 6 vertices.
What is the sum of all interior angles of a hexagon?
The sum of all interior angles of a hexagon is 720°.
How many diagonals does a hexagon have?
A hexagon has 9 diagonals.
Does a hexagon always have equal sides?
No, hexagons can have sides with different lengths. Regular hexagon has all sides are equal in length.
Are all six-sided shapes hexagon?
Yes, all six sided shapes are called hexagons.
