Perimeter of a Parallelogram

Geometry is a branch of mathematics that deals with the study of different geometrical shapes. It is of two types:

• Two-dimensional Geometry
• Three-dimensional Geometry

A parallelogram is a two-dimensional geometric shape bounded by four sides. The pair of opposite sides of a parallelogram are parallel and equal to each other. A parallelogram is slightly different from a rectangle in terms of vertical angles. In a rectangle, the measure of the vertical angle is 90°. But in a parallelogram, it is not necessarily equal to 90°. In this article, let us discuss what is the perimeter of a parallelogram, formula, and how to find the parallelogram perimeter with examples.

Table of Contents:

• • Definition
  • Formula
  • Base and Height
  • Relation Between Area and Perimeter
  • Examples

What is the Perimeter of a Parallelogram?

The perimeter is defined as the length of the boundaries of any shape. The sum of all the sides of a parallelogram is known as the perimeter of a parallelogram.  The parallelogram perimeter is similar to the perimeter of the rectangle. Since, both the shapes having similar properties, the area and the perimeter of the parallelogram have more or less same formulae. By adding all the boundaries or sides of the parallelogram, we can easily find the parallelogram perimeter.

Perimeter of a Parallelogram Formula

Let “a” and “b” be the sides of a parallelogram. Therefore, the perimeter of a parallelogram formula is as follows:

We know that the opposite sides of a parallelogram are parallel and equal to each other. Thus, the formula for finding the perimeter of a parallelogram is given by:

So, the perimeter of Parallelogram, P = a + b + a + b units

P = 2a +2b

P = 2(a+b)

Therefore, the perimeter of a parallelogram, P = 2(a+b) units

Perimeter of a parallelogram with Base and Height

The perimeter of the parallelogram with base and height is given using the property of the parallelogram. If “b” is the base of the parallelogram and “h” is the height of the parallelogram, then the formula is given as follows:

According to the property of the parallelogram, the opposite sides are parallel to each other, and the parallelogram perimeter is defined as two times of the base and height.

Thus, the formula for the perimeter of a parallelogram is:

P = 2 (b +h/cos θ)

where θ is the angle BAE, formed between the height and side of the parallelogram, i.e. AE and AB.

Area and Perimeter of a Parallelogram

We know that the area of a parallelogram is equal to the product of base and height.

A = b x h square units ……(1)

The relationship between the area and perimeter of a parallelogram is:

P = 2 (a+b) units

Therefore, the value of b in terms of P is

P/2 = a + b

b=(P/2) – a

Now, substitute the value of b in (1)

A = ((P/2) – a)h Square units

How to Find the Perimeter of a Parallelogram?

Go through the below example to find the perimeter of a parallelogram.

Example 1:

Find the perimeter of a parallelogram whose base and side lengths are 10cm and 5cm, respectively.

Solution:

Given:

Base length of a parallelogram = 10 cm

Side length of a parallelogram = 5 cm

We know that the perimeter of a parallelogram, P = 2(a+b) units.

Substitute the values

P = 2(10+5)

P = 2(15)

P = 30 cm

Therefore, the perimeter of a parallelogram is 30 cm.

Example 2:

Find the length of another side of the parallelogram whose base is 5 cm and the perimeter is 40 cm.

Solution:

Given:

Base, h = 5cm

Perimeter, p = 40cm

We know, that the perimeter of a parallelogram is,

p=2 (a+b) units

Now substitute the given values in the formula,

40 = 2 (a +5)

40 = 2a + 10

2a = 40-10

2a = 30

a = 30/2

a = 15 cm

Thus, the length of other side of the parallelogram is 15 cm.

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