Perimeter of a Parallelogram Formulas | List of Perimeter of a Parallelogram Formulas You Should Know - BYJUS

# Perimeter of a Parallelogram Formulas

The perimeter of an enclosed shape is the sum of the length of its boundaries. The perimeter of a parallelogram is equal to the sum of its four sides. In this article, we will learn how to determine the perimeter of a parallelogram. We will also look at other scenarios to find the missing measurement, when the perimeter and the length of one of the sides of the parallelogram are already provided....Read MoreRead Less

### Formula for the Perimeter of a Parallelogram

One of the distinguishing characteristics of a parallelogram is that the opposite sides are equal and parallel to each other.

Here, $$a$$ and $$b$$ are the sides of a parallelogram.

The perimeter of the parallelogram in the image is given as:

Perimeter, $$P = a+b+a+b$$

$$~~~~~~~~~~~~~~~~~~~~~= 2 (a + b)$$

### Rapid Recall

Perimeter of a parallelogram, $$P = 2(a + b)$$ units

### Solved Examples

Example 1: The base of a parallelogram is $$9$$ cm and one side is $$13$$ cm in length. Find the perimeter of the parallelogram.

Solution:

The measure of the sides of the parallelogram are:

Base, $$b = 9$$ cm

Side length, $$a = 13$$ cm

Perimeter of the parallelogram, $$P = 2(a + b)$$             [Formula for the perimeter of a parallelogram]

$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~= 2(13 + 9)$$            [Substitute $$13$$ for $$a$$ and $$9$$ for $$b$$]

$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~= 2 \times 22$$ cm           [Simplify]

$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~= 44$$ cm

Hence, the perimeter of the given parallelogram is $$44$$ cm.

Example 2: A parallelogram was cut exactly at the middle of its longest side to form two parallelograms. What is the length of the smaller  parallelogram, provided that the side that was not cut is $$16$$ cm and the perimeter of the large parallelogram is $$120$$ cm.

Solution:

Perimeter of the larger parallelogram $$= 120$$

So, the perimeter of the smaller parallelogram, $$P = \frac{120}{2} = 60$$ cm

Length of one side of the smaller parallelogram, $$a = 16$$ cm

Perimeter of a parallelogram,

$$P = 2(a + b)$$             [Formula for the perimeter of a parallelogram]

$$60 = 2(16 + b)$$           [Substitute $$16$$ for $$a$$ and $$60$$ for $$P$$]

$$\frac{60}{2} = 16 + b$$               [Divide by $$2$$]

$$30 = 16 + b$$               [Simplify]

$$30~-~16 = b$$

$$b = 14$$

Hence, the length of the smaller parallelogram is $$14$$ cm.

Example 3: Shawn and Macy were cutting a chocolate bar in the shape of a parallelogram. What would be the longer side of the parallelogram if the perimeter of the chocolate bar is $$16$$ cm and one of its shorter sides is $$3$$ cm.

Solution:

Perimeter, $$P = 16$$ cm

Smaller side, $$a = 3$$ cm

Perimeter of a parallelogram,

$$P = 2(a + b)$$              [Formula for the perimeter of a parallelogram]

$$16 = 2(3 + b)$$              [Substitute $$3$$ for $$a$$ and $$16$$ for $$P$$]

$$16 = 6 + 2b$$                 [Simplify]

$$16~-~6 = 2b$$

$$10 = 2b$$

$$b = \frac{10}{2} = 5$$ cm

Therefore, the longer side of the parallelogram is $$5$$ cm.