Perimeter of a Polygon – Definition with Examples

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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:

polygon

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. 

hexagon

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?

pentagon

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:

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

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 cm2. Find its perimeter.

Area of square = 100 cm2

Formula for area of square = Side  Side

As, 100 = Side  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

Attend this Quiz & Test your knowledge.

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?

30 cm
33 cm
26 cm
34 cm
CorrectIncorrect
Correct answer is: 33 cm
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?

6 cm
24 cm
12 cm
18 cm
CorrectIncorrect
Correct answer is: 18 cm
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?

63 cm
16 cm
32 cm
2 cm
CorrectIncorrect
Correct answer is: 32 cm
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?

30 cm
42 cm
36 cm
34 cm
CorrectIncorrect
Correct answer is: 30 cm
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

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

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

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.


Perimeter of a Polygon – Definition with Examples

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