 # 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°.

## How to Calculate 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.

## 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.

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

### Relation Between 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

### Example

Question:

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

Solution:

Given:

Base of a parallelogram = 10 cm

Height 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

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