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]