# Regular Hexagon

A **regular hexagon** is a closed shape polygon which has six equal sides and six equal angles. In case of any regular polygon, all its sides and angles are equal. For instance, a **regular pentagon** has 5 equal sides and a **regular octagon** has 8 equal sides. When such conditions are not met, polygons may resemble a variety of irregular shapes. When we arrange six equilateral triangles side by side, then a regular hexagon is composed. Then, the area of the regular hexagon becomes equal to six times the area of the same triangle.

## Regular Hexagon Properties

- It has 6 equal sides and 6 equal angles.
- It has 6 vertices.
- Sum of interior angles equals 720°.
- Interior angle is 120° and exterior angle is 60°.
- It is made up of six equilateral triangles.
- 9 diagonals can be drawn inside a regular hexagon.
- All the sides opposite to each other are parallel.

## Area and Perimeter of Regular Hexagon

We have thrown light on the definition and properties of regular hexagon till now, let us learn about its area and perimeter.

**Area of Regular Polygon** is given by;

A = 3√3/2 × a |

Where a is the measurement of its sides or length of the side.

**Perimeter of Hexagon** is equal to;

P = 6a |

where a is the side length.

## Angles of Regular Hexagon

As we already know, the sum of the angles of the regular hexagon which has all its 6 sides equal is 720°. Therefore, it’s interior angle and exterior angle is given by;

Each interior angle = 720°/6 = 120°

Each exterior angle = 180°- interior angle = 180°-120° = 60°

### Examples

**Q.1: Find the area and perimeter of hexagon, if all its sides have a length equal to 6cm.**

**Solution:** From the area and perimeter formula of a regular hexagon, we know;

Area = 2.59807 a^{2} = 2.59807 × 6^{2} = 93.53 cm^{2}

Perimeter = 6a = 6 × 6 = 36 cm

**Q.2: Evaluate the length of the side of a regular hexagon if its perimeter is given as 48cm.**

**Solution:** Given, perimeter = 48cm

By the formula, we know;

Perimeter = 6a

Therefore,

48 = 6a

Or

a = 48/6 = 8cm

Hence the length of the side to given hexagon is 8 cm