## Perimeter of a Polygon

**Polygon**

Polygon refers to a closed 2D shape which is made up of a finite number of line segments. The number of vertices of a polygon is always equal to the number of line segments. Examples of polygons are:

**Perimeter of a Polygon**

The total distance of the outer sides of a closed figure is known as the perimeter. It is the total length of all sides of a polygon.

Perimeter = Sum of all sides |

The unit of the perimeter of any polygon will remain the same as the unit of its respective sides. If the sides are given in different units, then convert them to the same unit and then find the perimeter.

## Perimeter of a Regular Polygon

A regular polygon has all sides equal. Therefore, we can find the perimeter of a regular polygon by repeated addition. So, we add the same length ‘n’ times if there are ‘n’ sides in the polygon.

Perimeter of a regular polygon = (length of one side) × number of sides |

**Example 1**: Find the perimeter of a regular hexagon with a 4 cm long side.

The perimeter of a regular polygon = (length of one side) × number of sides

Perimeter of a regular hexagon = 4 cm × 6

= 24 cm

**Example 2**: A pentagon has all sides equal to 6 cm. What will be its perimeter?

All the sides of the pentagon are equal. Therefore, it is a regular polygon.

The perimeter of a regular polygon = (length of one side) × number of sides

Perimeter of a regular pentagon = 6 cm × 5

= 30 cm

**Perimeter of an Irregular Polygon**

It is the total distance around a polygon. It can be found by adding together all the sides of the polygon.

**Example 1**: Work out the perimeter of the following rectangle:

Perimeter = Sum of all the sides

Perimeter of rectangle = Length + Width + Length + Width

Perimeter of the rectangle = 15 cm + 7 cm + 15 cm + 7 cm = **44 cm**

Hence, the formula of the perimeter of a rectangle:

Perimeter = 2 × length + width |

**Example 2**: Work out the perimeter of the following polygon:

Perimeter = Sum of the length of all the sides

= 13 cm + 3.5 cm + 3.5 cm + 13 cm + 4 cm = 37 cm

**Example 5**: Area of a square is given as 100 cm^{2}. Find its perimeter.

Area of square = 100 cm^{2}

Formula for area of square = Side x Side

As, 100 = Side x Side

Hence, Side = 10 cm

Perimeter of a Square = Side + Side + Side + Side = 4 Sides

= 4 × 10 = 40 cm

Fun Facts– The headquarters of the US Department of Defense is called “The Pentagon” because unlike other buildings which have only four sides it has five sides. |

## Practice Problems

## Perimeter of a Polygon

### 1Four of the sides of an irregular Hexagon measure 5 cm. The measures of the other two sides are 6 cm and 7 cm. What is the perimeter of the hexagon?

Perimeter of an irregular polygon = sum of all sides

Perimeter of the given hexagon = 5 cm + 5 cm + 5 cm + 5 cm + 6 cm + 7 cm = 33 cm.

### 2An irregular polygon with three sides has its sides measurements given as 4 cm, 8 cm, and 6 cm. What is the perimeter of the polygon?

Perimeter of an irregular polygon = sum of all sides

Perimeter of the given polygon = 4 cm + 6 cm + 8 cm = 18 cm.

### 3A rectangle has a length equal to 7 cm and a width equal to 9 cm. What is the perimeter of the rectangle?

Perimeter of a rectangle = length + width + length + width

Perimeter of given rectangle = 7 cm + 9 cm + 7 cm + 9 cm = 32 cm.

### 4One of the sides of a regular pentagon measures 6 cm. What is the perimeter of the pentagon?

A regular pentagon has 5 sides of the same length.

Perimeter of a regular polygon = number of sides × length of a side.

Perimeter of the given regular pentagon = 5 × 6 cm = 30 cm.

## Frequently Asked Questions

**How to find the perimeter of a polygon?**

To find the perimeter of a polygon, add the lengths of all the sides of the polygon.

**What is the formula for the perimeter of a polygon?**

The perimeter of a regular polygon can be found by multiplying the length of a side by the number of sides. It’s important to note that this formula only works for regular polygons.

**How to find the perimeter of a regular polygon with n sides?**

Multiply the length of one side by n. Perimeter = n x (length of a side)

**Where do we find perimeter in real-life situations?**

We calculate the perimeter when installing a fence around a garden or a piece of land. We also need to find the perimeter while building a swimming pool, putting up Christmas lights around the house, etc.