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 = 2(a+b) 

 
b = base length  ,  

a = adjacent side length  

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 “\theta\\;\;\;\;\;”is the angle between the height CE and side CA of the parallelogram. If we apply cos\theta\\;\;\;\; to triangle ACE, we get,

\cos\theta=\frac ha\\;\;\;\;\; a=\frac h{\cos\theta}\\;\;\;\;\;

 

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

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

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Azhar Ali

Azhar Ali

Mathematician and Blogger.

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