## 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* = 6*a*

## 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

## Hexagon

### 1What 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

^{°}.

### 2A plane with six sides is classified as

Hexagon is a two dimensional polygon with six sides.

### 3The 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

^{°}.

### 4A 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.

**F**requently Asked Questions

**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.