106 LearnersLast updated on July 25th, 2025
Perimeter of Parallelogram
The perimeter of a shape is the total length of its boundary. The sum of all four sides is called the perimeter of a parallelogram. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of a parallelogram.
What is the Perimeter of a Parallelogram?
The perimeter of a parallelogram is the total length of its four sides. By adding the length of all four sides, we get the perimeter of the shape. The formula for the perimeter of a parallelogram is 𝑃 = 2𝑎 + 2𝑏, where a and b are the lengths of the adjacent sides of the parallelogram. For instance, if a parallelogram has sides, a = 6, b = 8, then its perimeter is 𝑃 = 2(6) + 2(8) = 28.
Formula for Perimeter of Parallelogram - 𝑷 = 2𝑎 + 2𝑏.
Let’s consider another example of a parallelogram with side lengths, 𝑎 = 8, 𝑏 = 10. So the perimeter of the parallelogram will be: 𝑷 = 2𝑎 + 2𝑏 = 2(8) + 2(10) = 16 + 20 = 36.
How to Calculate the Perimeter of Parallelogram
To find the perimeter of a parallelogram, we just need to apply the given formula and sum the lengths of all the sides. For instance, a given parallelogram has the sides of a = 7 and b = 9. Perimeter = 2a + 2b = 2(7) + 2(9) = 14 + 18 = 32 cm. Example Problem on Perimeter of Parallelogram - For finding the perimeter of a parallelogram, we use the formula, 𝑷 = 2𝑎 + 2𝑏. For example, let’s say, a = 5 cm, b = 4 cm. Now, the perimeter = 2(5) + 2(4) = 10 + 8 = 18 cm. Therefore, the perimeter of the parallelogram is 18 cm.
Tips and Tricks for Perimeter of Parallelogram
Learning some tips and tricks makes it easier for children to calculate the perimeter of parallelograms. Here are some tips and tricks given below: Always remember that a parallelogram's perimeter is simply the sum of twice the lengths of the two distinct sides. For that, use the formula, 𝑷 = 2𝑎 + 2𝑏. Calculating the perimeter of a parallelogram starts by determining the length of each side. The side lengths can often be found using coordinate geometry if vertices are given. To reduce confusion, arrange the indicated side lengths if you need the perimeter of a group of parallelograms. After that, apply the formula to each parallelogram. To avoid mistakes when adding the perimeter, ensure the side lengths are precise and constant for common uses like gardening and architecture. If you are given the semi-perimeter, which is half the perimeter, you can multiply it by 2 to determine the full perimeter. The semi-perimeter is not commonly used in parallelogram-related calculations as it is in triangles.
Common Mistakes and How to Avoid Them in Perimeter of Parallelogram
Did you know that while working with the perimeter of a parallelogram, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Confusing the formula for perimeter with the formula for area.
Remember that the perimeter involves adding up the lengths of the sides, while the area involves multiplication of base and height. For a perimeter, use 𝑷 = 2𝑎 + 2𝑏.
Mistake 2
Students may confuse the concepts of area and perimeter, leading to incorrect calculations.
It is important to note that the perimeter, calculated in linear units, is the total length of the parallelogram’s sides, while the area, in square units, represents the space inside the parallelogram.
Mistake 3
Assuming that every parallelogram is a rectangle, which results in inaccurate calculations.
A parallelogram can have different angles and side lengths. Be careful about the specific shape to ensure accurate calculations.
Mistake 4
Using the wrong values for the length of the sides, misreading a problem, or mislabeling the sides.
Double-check the problem and ensure that you're using the correct lengths for your parallelogram.
Mistake 5
Misunderstanding or misidentifying the side lengths that are given in a problem outline.
Before starting the calculations, make sure that you understand the problem and, if it's possible, try to sketch the parallelogram to accurately identify the side lengths.
Perimeter of Parallelogram Examples
Problem 1
A rectangular garden has a perimeter of 48 meters with two sides measuring 12 meters each. Find the length of the other two sides.
Length of the other two sides = 12 meters each.
Explanation
Let ‘b’ be the length of the unknown sides. The given perimeter = 48 meters. Length of the known sides = 12 meters each. Perimeter of the parallelogram = 2(a + b). 48 = 2(12 + b) 48 = 24 + 2b 24 = 2b b = 12 Therefore, the length of the other two sides is 12 meters each.
Problem 2
A wire with a perimeter of 200 inches is reshaped into a rectangular frame. If one side of the rectangle is 60 inches, find the length of the other side.
40 inches
Explanation
Given that the perimeter of the rectangle is equal to the total length of the wire: Length of one side = 60 inches. Perimeter of the rectangle = 2(l + b) 200 = 2(60 + b) 200 = 120 + 2b 80 = 2b b = 40 Therefore, the length of the other side is 40 inches.
Problem 3
Find the perimeter of a parallelogram whose sides are 14 cm and 9 cm.
46 cm
Explanation
Perimeter of parallelogram = 2a + 2b 𝑃 = 2(14) + 2(9) = 28 + 18 = 46 Therefore, the perimeter of the parallelogram is 46 cm.
Problem 4
Emily is planning a parallelogram-shaped flower bed in her yard. She measures the two distinct sides of the bed: Side A = 10 meters Side B = 7 meters How much fencing does Emily need to buy to go around the edge of the bed?
Emily will need 34 meters of fencing to go around the bed.
Explanation
The perimeter of a parallelogram is the sum of twice the lengths of the two distinct sides. Using the formula: 𝑃 = 2a + 2b 𝑃 = 2(10) + 2(7) = 20 + 14 = 34 meters.
Problem 5
Find the perimeter of a parallelogram with sides a = 13 cm and b = 5 cm.
36 cm
Explanation
Perimeter of the parallelogram = 2a + 2b 𝑃 = 2(13) + 2(5) = 26 + 10 = 36 cm. Therefore, the perimeter of the parallelogram is 36 cm.
FAQs on Perimeter of Parallelogram
1.Evaluate the parallelogram’s perimeter if its sides are 8 cm and 6 cm.
2.What is meant by a parallelogram’s perimeter?
3.What are the types of parallelograms?
4.Which parallelogram has all sides equal?
5.How do you find the perimeter of a rectangle?
Important Glossaries for Perimeter of Parallelogram
Perimeter: The total length of the sides of a shape. Parallelogram: A quadrilateral with opposite sides parallel and equal in length. Formula of perimeter: The mathematical expression used to calculate the perimeter of a parallelogram is 𝑷 = 2𝑎 + 2𝑏. Rectangle: A parallelogram with four right angles. Rhombus: A parallelogram with all sides of equal length.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
