102 LearnersLast updated on July 25th, 2025
Perimeter of Quadrilateral
The perimeter of a shape is the total length of its boundary. The sum of all four sides is called the perimeter of a quadrilateral. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of a quadrilateral.
What is the Perimeter of a Quadrilateral?
The perimeter of a quadrilateral 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 quadrilateral is ๐ = ๐ + ๐ + ๐ + ๐, where a, b, c, and d are the sides of the quadrilateral. For instance, if a quadrilateral has sides, a = 5, b = 7, c = 9, and d = 4, then its perimeter is ๐ = 5 + 7 + 9 + 4 = 25.
Formula for Perimeter of Quadrilateral - ๐ = ๐ + ๐ + ๐ + ๐.
Letโs consider another example of a quadrilateral with side lengths, ๐ = 8, ๐ = 6, ๐ = 10, and ๐ = 5. So the perimeter of the quadrilateral will be: ๐ = ๐ + ๐ + ๐ + ๐ = 8 + 6 + 10 + 5 = 29.
How to Calculate the Perimeter of Quadrilateral
To find the perimeter of a quadrilateral, we just need to apply the given formula and sum all the sides of the quadrilateral. For instance, a given quadrilateral has sides of a = 7, b = 8, c = 5, d = 6. Perimeter = sum of all sides = 7 + 8 + 5 + 6 = 26 cm. Example Problem on Perimeter of Quadrilateral - For finding the perimeter of a quadrilateral, we use the formula, ๐ = ๐ + ๐ + ๐ + ๐. For example, letโs say, a = 10 cm, b = 3 cm, c = 4 cm, and d = 9 cm. Now, the perimeter = sum of all sides = 10 + 3 + 4 + 9 = 26 cm. Therefore, the perimeter of the quadrilateral is 26 cm.
Tips and Tricks for Perimeter of Quadrilateral
Learning some tips and tricks makes it easier for children to calculate the perimeter of quadrilaterals. Here are some tips and tricks given below: Always remember that a quadrilateral's perimeter is simply the sum of the four sides of the shape. For that, use the formula, ๐ = ๐ + ๐ + ๐ + ๐. Calculating the perimeter of a quadrilateral starts by determining the length of each side using the distance formula. The distance formula is: Distance = โ((x2-x1)ยฒ + (y2-y1)ยฒ). Here, (x1, y1) and (x2, y2) indicate the positions of two points that make up a side of the quadrilateral. Calculate the lengths of all sides and sum them. To reduce confusion, specifically arrange the indicated side lengths if you need the perimeter of a group of quadrilaterals. After that, apply the formula to each quadrilateral. To avoid mistakes when adding the perimeter, make sure 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.
Common Mistakes and How to Avoid Them in Perimeter of Quadrilateral
Did you know that while working with the perimeter of a quadrilateral, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Incorrectly using formulas meant for triangles.
Remember that formulas for triangles, such as the Pythagorean theorem, do not apply to quadrilaterals. Sum the lengths of all four sides to find the perimeter.
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 quadrilateralโs sides, while the area, in square units, represents the space inside the quadrilateral.
Mistake 3
Assuming that every quadrilateral is a rectangle or square, which results in inaccurate calculations.
Quadrilaterals can have a variety of side lengths and shapes. Always pay attention to the type of quadrilateral 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 quadrilateral.
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 draw a quadrilateral to accurately identify the side lengths.
Perimeter of Quadrilateral Examples
Problem 1
A rectangular garden has a perimeter of 72 meters and a width of 10 meters. To find out the length of the garden, subtract twice the width from the total perimeter and then divide by 2.
Length of the garden = 26 meters.
Explanation
Let โlโ be the length of the garden. And the given perimeter = 72 meters. Width = 10 meters. Perimeter of rectangle = 2 ร (length + width) 72 = 2 ร (l + 10) 72 = 2l + 20 2l = 72 โ 20 = 52 l = 52 รท 2 = 26 Therefore, the length of the garden is 26 meters.
Problem 2
A wire with a perimeter of 400 inches is reshaped into a square. Find the length of each side of the square.
100 inches
Explanation
Given that the perimeter of the wire equals the perimeter of the square, here is the solution: Perimeter of the square = 4 ร side 400 = 4 ร side 400 รท 4 = 100 side = 100 Therefore, the length of each side of the square is 100 inches.
Problem 3
Find the perimeter of a rhombus with sides of 15 cm.
60 cm
Explanation
Perimeter of rhombus = 4 ร side P = 4 ร 15 = 60 Therefore, the perimeter of the rhombus is 60 cm.
Problem 4
Lucy is planning a quadrilateral picnic area in her backyard. She measures the four sides of the area: Side A = 14 meters Side B = 11 meters Side C = 13 meters Side D = 9 meters How much fencing should Lucy buy to go around the edge of the area?
Lucy will need 47 meters of fencing to go around the picnic area.
Explanation
The perimeter of a quadrilateral is the sum of all the four sides. Using the formula: P = a + b + c + d P = 14 + 11 + 13 + 9 = 47 meters.
Problem 5
Find the perimeter of a kite with sides of a = 12, b = 12, c = 8, and d = 8.
Perimeter = a + b + c + d = 12 + 12 + 8 + 8 = 40 meters.
Explanation
Each pair of opposite sides in the kite has equal length. The entire distance around the kite is calculated to be 40 meters by summing the lengths of the four sides.
FAQs on Perimeter of Quadrilateral
1.Evaluate the quadrilateralโs perimeter if its sides are 5 cm, 10 cm, 15 cm, and 20 cm.
2.What is meant by a quadrilateralโs perimeter?
3.What are the types of quadrilaterals?
4.Which quadrilateral has all sides equal?
5.Which quadrilateral has the smallest perimeter given equal side lengths?
Important Glossaries for Perimeter of Quadrilateral
Perimeter: The total length of the sides of a shape. Quadrilateral: A polygon with four sides and four angles. Formula of perimeter: The mathematical expression used to calculate the perimeter of a quadrilateral is ๐ = ๐ + ๐ + ๐ + ๐. Rectangle: A quadrilateral with opposite sides equal and all angles 90 degrees. Square: A quadrilateral with all sides equal and all angles 90 degrees.
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
