108 LearnersLast updated on August 5th, 2025
Perimeter of Cuboid
The perimeter of a shape is the total length of its boundary. For a cuboid, the perimeter refers to the total distance around its edges. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of a cuboid.
What is the Perimeter of a Cuboid?
The perimeter of a cuboid is the total length around its edges. By adding the lengths of all the edges, we get the perimeter of the shape. The formula for the perimeter of the edges of a cuboid is 𝑃 = 4(l + w + h), where l, w, and h are the length, width, and height of the cuboid. For instance, if a cuboid has dimensions, l = 6, w = 4, and h = 10, then its perimeter is P = 4(6 + 4 + 10) = 80.
Formula for Perimeter of Cuboid - 𝑃 = 4(l + w + h)
Let’s consider another example of a cuboid with dimensions, 𝑙 = 5, 𝑤 = 3, and 𝑏 = 2. So the perimeter of the cuboid's edges will be: 𝑃 = 4(l + w + h) = 4(5 + 3 + 2) = 40.
How to Calculate the Perimeter of a Cuboid
To find the perimeter of a cuboid, we just need to apply the given formula and sum all the edges of the cuboid. For instance, a given cuboid has dimensions of l = 7, w = 3, h = 5. Perimeter = 4(l + w + h) = 4(7 + 3 + 5) = 60 cm. Example Problem on Perimeter of Cuboid - For finding the perimeter of a cuboid, we use the formula, 𝑃 = 4(l + w + h). For example, let’s say, l = 6 cm, w = 4 cm, and h = 3 cm. Now, the perimeter = 4(l + w + h) = 4(6 + 4 + 3) = 52 cm. Therefore, the perimeter of the cuboid is 52 cm.
Tips and Tricks for Perimeter of Cuboid
Learning some tips and tricks makes it easier for children to calculate the perimeter of cuboids. Here are some tips and tricks given below: Always remember that a cuboid's perimeter is simply the sum of the lengths of all the edges. For that, use the formula, 𝑃 = 4(l + w + h). Calculating the perimeter of a cuboid starts by determining the length of each edge of the shape. The dimensions can be found by measuring or given data. To reduce confusion, specifically arrange the indicated dimensions if you need the perimeter for multiple cuboids. After that, apply the formula to each cuboid. To avoid mistakes when adding the perimeter, make sure the dimensions are precise and constant for common uses like construction and design. 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 Cuboid
Did you know that while working with the perimeter of a cuboid, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Incorrectly using the volume formula for calculating the perimeter.
Remember that the volume and perimeter are different. The volume is calculated by multiplying the dimensions, while the perimeter is calculated by summing the edge lengths using the formula 𝑃 = 4(l + w + h).
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 around the cuboid’s edges, while the surface area, in square units, represents the total area of all faces of the cuboid.
Mistake 3
Assuming the cuboid is a cube, which results in inaccurate calculations.
A cuboid can have different lengths, widths, and heights. Always be careful about the cuboid’s dimensions to ensure accurate calculations.
Mistake 4
Using the wrong values for the dimensions, misreading a problem, or mislabeling the dimensions.
Double-check the problem and ensure that you're using the correct dimensions for your cuboid.
Mistake 5
Misunderstanding or misidentifying the dimensions that are given in a problem outline.
Before starting the calculations, make sure that you understand the problem and, if possible, try to sketch the cuboid to accurately identify the dimensions.
Perimeter of Cuboid Examples
Problem 1
A rectangular gift box has a perimeter of 64 cm around its edges. If the length is 10 cm and the width is 8 cm, what is the height of the box?
Height of the box = 4 cm.
Explanation
Let ‘h’ be the height of the box. And the given perimeter = 64 cm. Length = 10 cm, Width = 8 cm. Perimeter of cuboid = 4(l + w + h). 64 = 4(10 + 8 + h) 64 = 4(18 + h) 64 ÷ 4 = 18 + h 16 = 18 + h h = 16 – 18 h = 4 Therefore, the height of the box is 4 cm.
Problem 2
A metal frame is reshaped into a cuboid with a perimeter of 72 inches. If the length and width are equal, and each measures 6 inches, find the height of the cuboid.
Height of the cuboid = 6 inches.
Explanation
Given that the perimeter of the cuboid is 72 inches and the length equals the width: Perimeter of cuboid = 4(l + w + h). 72 = 4(6 + 6 + h) 72 = 4(12 + h) 72 ÷ 4 = 12 + h 18 = 12 + h h = 18 – 12 h = 6 Therefore, the height of the cuboid is 6 inches.
Problem 3
Find the perimeter of a cuboid whose length is 8 cm, width is 5 cm, and height is 10 cm.
92 cm
Explanation
Perimeter of cuboid = 4(l + w + h) P = 4(8 + 5 + 10) = 92 Therefore, the perimeter of the cuboid is 92 cm.
Problem 4
Tim is building a bookshelf in the shape of a cuboid. The dimensions are as follows: Length = 12 meters, Width = 7 meters, Height = 4 meters. How much material does Tim need to cover the edges of the bookshelf?
Tim will need 92 meters of material to cover the edges.
Explanation
The perimeter of a cuboid is the sum of all the edges. Using the formula: P = 4(l + w + h) P = 4(12 + 7 + 4) = 92 meters.
Problem 5
Find the perimeter of a cuboid where the dimensions are: l = 9, w = 6, h = 3.
Perimeter = 72 cm.
Explanation
The perimeter of the cuboid is calculated by summing the lengths of all the edges. Perimeter = 4(l + w + h) = 4(9 + 6 + 3) = 72 cm.
FAQs on Perimeter of Cuboid
1.Evaluate the cuboid’s perimeter if its dimensions are l = 3 cm, w = 5 cm, and h = 7 cm.
2.What is meant by a cuboid’s perimeter?
3.What are the types of cuboids?
4.Which shape is a special type of cuboid with equal dimensions?
5.Which cuboid has the smallest perimeter for a given volume?
Important Glossaries for Perimeter of Cuboid
Perimeter: The total length around the edges of a shape. Cuboid: A three-dimensional shape with six rectangular faces. Formula of perimeter: The mathematical expression used to calculate the perimeter of a cuboid is 𝑃 = 4(l + w + h). Length: The longest dimension of a cuboid. Width: The dimension of a cuboid perpendicular to the length.
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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
