how to find the perimeter of a parallelogram

PERIMETER OF PARALLELOGRAM

In this page perimeter of parallelogram we are going to see some different kinds example problems to understand this topic.

In the below parallelogram ABCD we have two lengths and two widths. So we can write the formula to find perimeter of a parallelogram as follows.

Formula :

Perimeter of a parallelogram = 2 (L + W)

Here l represent length and w represents width

Example 1:

Find the perimeter of a parallelogram whose length is 15 cm and width is 12 cm.

Solution:

Perimeter of a parallelogram = 2 (L + W)

Here, length = 15 cm and breadth = 12 cm

= 2 ( 15 + 12 ) == > 2 (27) ==> 54 cm

Hence, perimeter of parallelogram is 54 cm.

Example 2:

Find the perimeter of parallelogram whose length is 9 cm and width is 3 cm.

Solution:

Perimeter of a parallelogram = 2 (L + W)

Here, length = 9 cm and breadth = 3 cm

= 2 ( 9 + 3 ) ==> 2 (12) ==> 24 cm

Hence, perimeter of parallelogram is 24 cm.

Example 3:

Prove that the vertices (5,8) (6,3) (3,1) (2,6) form a parallelogram and also find the perimeter.

Solution:

Let the given points as A (5,8), B (6,3), C(3,1) and D(2,6). By the definition of a parallelogram if the length of opposite sides will be equal, then it is parallelogram. So first let us find the length of all sides

Distance between two points = √(x₂ - x₁)² + (y₂ - y₁)²

Length of AB

A (5,8) B (6,3)

x₁ = 5, y₁ = 8

x₂ = 6, y₂ = 3

length of AB = √(6 - 5)² + (3 - 8)²

= √(1)² + (-5)² ==> √1 + 25 = √26 -------- (1)

Length of BC

B (6,3) C (3,1)

x₁ = 6 y₁ = 3

x₂ = 3 y₂ = 1

length of AB = √(3 - 6)² + (1 - 3)²

= √(-3)² + (-2)² ==> √9 + 4 = √13 -------- (2)

Length of CD

C (3,1) D (2,6)

x₁ = 3 y₁ = 1

x₂ = 2 y₂ = 6

length of AB = √(2 - 3)² + (6 - 1)²

= √(-1)² + (5)² ==> √1 + 25 = √26 -------- (3)

Length of DA

D (2,6) A (5,8)

x₁ = 2 y₁ = 6

x₂ = 5 y₂ = 8

length of AB = √(5 - 2)² + (8 - 6)²

= √(3)² + (2)² ==> √9 + 4 = √13 -------- (4)

The opposite sides are having equal length.From this we can conclude that the given vertices form a parallelogram.

length of parallelogram = √26

width of parallelogram = √13

Perimeter of a parallelogram = 2 (L + W)

= 2 (√26 + √13) cm

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