How to Find the Perimeter of a Parallelogram

A quadrilateral has two diagonals and four equal sides with opposite sides equal called a parallelogram. In a parallelogram its sides never intersect but its diagonal intersects each other at the center point. The diagonal divides the parallelogram into two equal parts. 

A parallelogram is a two-dimensional figure, and you can calculate its perimeter using the concept of mensuration. Mensuration involves calculating lengths, areas, perimeters, volumes, etc. of geometrical figures.    

Parallelogram Properties 

  • The opposite sides of a rectangle are congruent 
  • Angles opposite each other are congruent 
  • All angles are right if one angle is right. 
  • Parallelograms are bisected by their diagonals. 

The Perimeter of a Parallelogram When Two Adjacent Sides Are Given

Parallelogram perimeters are calculated using the same formula as rectangle perimeters. Parallelograms have equal opposite sides, just like rectangles.

Perimeter of Parallelogram =[katex] 2(a+b) [/katex]

[katex] b = base length  [/katex],  

 [katex] a = adjacent side length  [/katex] 

Perimeter of a Parallelogram When the Base, Height and Angle Are Given

The formula for the perimeter of a parallelogram when the base, height, and angle are given is derived using the properties of a parallelogram. Consider the picture below.

Here, “h” is the height and “b” is the base of the parallelogram while [katex] “\theta\\;\;\;\;\;”[/katex]is the angle between the height CE and side CA of the parallelogram. If we apply [katex] cos\theta\\;\;\;\; [/katex] to triangle ACE, we get,

[katex] \cos\theta=\frac ha\\;\;\;\;\; [/katex]

[katex] a=\frac h{\cos\theta}\\;\;\;\;\; [/katex]


Therefore, the formula of the perimeter of a parallelogram when the base, height, and angle are known can be written as:

Perimeter of parallelogram= [katex] 2(\frac h{\cos\theta}+b)\\;\;\;\;\; [/katex]

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