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

**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

**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 -------- (1)

Since opposite sides have equal length then the vertices form a parallelogram

length of parallelogram = √26

width of parallelogram = √13

Perimeter of a parallelogram = 2 (L + W)

= 2 (√26 + √13) cm

**Related Topics**

**perimeter of sector****Length of arc****Practice questions on length of arc****Perimeter of square****Perimeter of parallelogram****Perimeter of rectangle****Perimeter of triangle****Area of a circle****Area of Semicircle****Area of Quadrant****Area of sector****Area of triangle****Area of equilateral triangle****Area of scalene triangle****Area of square****Area of rectangle****Area of parallelogram****Area of rhombus****Area of trapezium****Area of quadrilateral****Area around circle****Area of pathways****Area of combined shapes**

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