- Home
- >
- Perimeters of Polygons â€“ Explanation & Examples

# Perimeters of Polygons â€“ Explanation & Examples

Have you ever walked around the edge of a school compound or a park? After completion of a whole round, the distance traveled by you will be exactly equal to the perimeter of the compound or the park.

Therefore,** the perimeter of a polygon is defined as the total distance around the outside of a polygon.Â The perimeter of a polygon is measured in meters, kilometers, yards, etc. **

This article will show how to calculate the perimeter of polygons such as triangle, rectangle, square, parallelogram, rhombus, and trapezoid. Â We will also discuss the formulas for calculating the perimeter of different polygons with examples.

## How to Find the Perimeter of a Polygon?

By definition,** the perimeterÂ of a polygon is calculated by taking the sum of all side lengths of a particular polygon. You can also find the perimeter of all polygons, whether they are regular or irregular polygons.**

For a regular polygon, the perimeter is equal to the product of one side length and the number of sides of the polygon.

**Perimeter of a regular polygon = (length of one side) Ã— number of sides**

For example, the perimeter of a regular pentagon whose side length 8 cm, is given by;

Perimeter of a regular pentagon = 8 x 5 = 40 cm.

**For an irregular polygon, the perimeter is calculating by adding together the individual side lengths.**

For example, the perimeter of an irregular pentagon whose side lengths are; 5 cm, 4 cm, 6 cm, 10 cm, and 9 cm.

Perimeter = (5 + 4 + 6 + 10 + 9) cm

= 34 cm.

## What is the formula for finding the perimeter of different polygons?

Different types of regular polygons have their own formulas for calculating perimeter. Letâ€™s take a look.

### Perimeter of triangles

The perimeter of a triangle is given by;

**P = a + b + c**

For an equilateral triangle**, the perimeter = 3a**

Where a, b, and c are the three side lengths of a triangle.

*Example 1*

Find the perimeter of a triangle whose sides are 20 cm, 15 cm, and 18 cm.

__Solution__

Perimeter of a triangle = a + b + c

= (20 + 15 + 18) cm

= 53 cm

*Example 2*

Calculate the perimeter of an equilateral triangle whose side length is 12 cm.

__Solution__

Perimeter of an equilateral triangle = 3a

= (3 x 12) cm

= 36 cm

*Example 3*

Determine the value of x for a triangle whose side lengths are, (x + 20) cm, (4x â€“ 5) cm, (2x + 15) cm and the perimeter is 100 cm.

__Solution__

Perimeter = a + b + c

(x + 20) + (4x â€“ 5) + (2x + 15) = 100 cm

Simplify.

x + 20 + 4x â€“ 5 + 2x + 15 = 100

Collect the like terms.

7x + 30 = 100

Subtract 30 on both sides.

7x = 70

Divide both sides by 7 to get,

x = 10.

Therefore, the value of x = 10 cm.

So, the three side lengths are;

â‡’ (x + 20) = (10 + 20) = 30 cm

â‡’ (4x â€“ 5) = 4(10) â€“ 5 = 35 cm

â‡’ (2x + 15) = 2(10) + 15 = 35 cm.

### The perimeter of a square and a rhombus

The perimeter of a square is given by,

**P = a + a + a + a**

**P= 4a**

Where a = the length of the side length of a square.

Since a square and a rhombus have 4 equal sides, then the perimeter of a rhombus is equal to a square’s perimeter.

*Example 4*

Calculate the perimeter of a square that has a length of 10 ft.

__Solution__

P= 4a

= (4 x 10) ft

= 40 ft.

*Example 5*

Find the perimeter of a rhombus with a side length of 4 inches.

Solution

Perimeter of a rhombus = 4a

= (4 x 4) inches.

### The perimeter of a rectangle and parallelogram

The perimeter of a rectangle and parallelogram are equal. The formula for calculating the perimeter of a rectangle is given by,

Perimeter of a rectangle =Â Length + Length + width + width

**Perimeter of a rectangle =Â ****2 (LÂ +Â W)**

where,

L = length of a rectangle or parallelogram and

W = width of the rectangle or parallelogram.

*Â Example 6*

What is the perimeter of a rectangle with a length of 100 mm and a width of 80 mm?

__Solution__

Perimeter of a rectangle =Â 2 (LÂ +Â W).

= 2 (100 + 80) mm

= 2 x 180 mm

P = 360 mm

*Example 7*

Find the perimeter of a parallelogram whose length is 12 yards and whose width is 5 yards.

__Solution__

Perimeter of a parallelogram =Â 2(LÂ +Â W).

= 2 (12 + 5) yards.

= 2 x 17 yards

P = 34 yards

*Example 8*

The width of a rectangle 5 m less than the length. Find the length and width of the rectangle if its perimeter is 34 m.

__Solution__

The width is 5 m less than the length.

Let, the length = x.

Width = x â€“ 5

But, the perimeter = 2 (L + W)

34 = 2 (x â€“ 5 + x)

34 = 2 (2x – 5)

34 = 4x -10

Add 10 on both sides.

44 = 4x

Divide both sides by 4.

x = 11

Therefore, the length of the rectangle is 11m, and the width is 6 m.

### The perimeter of a trapezoid

The perimeter of a trapezoid is given by,

P = a + b + c + d

where a, b, c, and d are the lengths of each side.

*Example 9*

Calculate the perimeter of the trapezoid shown below.

__Solution__

Perimeter of a trapezoid = a + b + c + d

= (25 + 30 + 22 + 10)

= 87 cm.

### Perimeter of irregular polygons

As stated earlier, the perimeter of an irregular polygon is equal to the sum of all side lengths.

*Example 10*

Calculate the perimeter of the diagram shown below if the dimensions are in mm.

__Solution__

Perimeter = (4 + 11 + 10 + 30 + 10 + 11 + 4 + 11 + 10 + 30+ 10 + 11) mm

P = 152 mm