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101 LearnersLast updated on September 13, 2025
Area of Cuboid
Area is the space inside the boundaries of a three-dimensional shape or surface. There are different formulas for finding the surface area of various shapes/figures. These are widely used in architecture and design. In this section, we will find the surface area of the cuboid.
What is the Surface Area of a Cuboid?
A cuboid is a three-dimensional figure with six rectangular faces, where opposite faces are equal. It has 12 edges and 8 vertices.
The surface area of the cuboid is the total area of all its six rectangular faces.
Surface Area of the Cuboid Formula
To find the surface area of a cuboid, we use the formula: 2(lb + bh + lh), where l is the length, b is the breadth, and h is the height. Now let’s see how the formula is derived. Derivation of the formula: A cuboid has three pairs of identical rectangular faces:
- Two faces with dimensions l and b.
- Two faces with dimensions b and h.
- Two faces with dimensions l and h. The area of each pair of identical faces is calculated as follows: - Area of faces with dimensions l and b: 2 × (l × b)
- Area of faces with dimensions b and h: 2 × (b × h)
- Area of faces with dimensions l and h: 2 × (l × h) By adding these areas, we obtain the total surface area: Surface Area = 2(lb + bh + lh)
How to Find the Surface Area of a Cuboid?
We can find the surface area of a cuboid using the formula 2(lb + bh + lh). This formula accounts for all six faces of the cuboid. Let's see an example of how this formula is applied.
For example, if the length, breadth, and height of a cuboid are 4 cm, 3 cm, and 2 cm respectively, then the surface area is: Surface Area = 2(lb + bh + lh) = 2(4×3 + 3×2 + 4×2) = 2(12 + 6 + 8) = 2 × 26 = 52 The surface area of the cuboid is 52 cm².
Unit of Surface Area of Cuboid
We measure the surface area of a cuboid in square units. The measurement depends on the system used:
In the metric system, the area is measured in square meters (m²), square centimeters (cm²), and square millimeters (mm²). In the imperial system, the area is measured in square inches (in²), square feet (ft²), and square yards (yd²).
Special Cases or Variations for the Surface Area of Cuboid
Since a cuboid is a three-dimensional shape with rectangular faces, its surface area can be calculated by considering various scenarios:
Case 1: All sides are different If the length, breadth, and height are different, use the formula Surface Area = 2(lb + bh + lh).
Case 2: Some sides are equal If two dimensions are equal, like a cube (where l = b = h), the formula simplifies to Surface Area = 6s², where s is the side length.
Case 3: One pair of opposite faces are squares If one pair of opposite faces are squares (e.g., length = breadth), apply the standard formula by substituting values.
Tips and Tricks for Surface Area of Cuboid
To ensure accurate results while calculating the surface area of a cuboid, consider the following tips and tricks:
- Double-check the dimensions provided to ensure they are correctly identified as length, breadth, and height.
- Remember that the surface area is concerned with all six faces, so ensure each pair of faces is accounted for.
- Use consistent units of measurement for all dimensions to avoid errors in calculation.
Common Mistakes and How to Avoid Them in Surface Area of Cuboid
It is common for students to make mistakes while finding the surface area of a cuboid. Let’s take a look at some mistakes made by students.
Mistake 1
Using the wrong dimensions in the formula
Ensure the dimensions for length, breadth, and height are correctly identified to avoid using incorrect values in the formula Surface Area = 2(lb + bh + lh).
Mistake 2
Measuring the area using the wrong units
For the area to be in square meters (m²), all dimensions should be in meters.
If they are in centimeters, convert them to meters before calculating.
Mistake 3
Confusing cuboid with cube
A cuboid has rectangular faces, whereas a cube has all square faces.
Ensure the correct shape is identified to use the appropriate formula.
Mistake 4
Ignoring one or more faces in calculation
Remember that a cuboid has six faces, and all must be included in the surface area calculation.
Double-check calculations to ensure all faces are accounted for.
Mistake 5
Multiplying dimensions instead of calculating face areas
Instead of multiplying all dimensions together, calculate the area of each face and sum them up using the formula 2(lb + bh + lh).
Surface Area of Cuboid Examples
Problem 1
A cuboid-shaped box has dimensions 5 m, 4 m, and 3 m. What will be the surface area?
We will find the surface area as 94 m²
Explanation
Here, the length, breadth, and height are 5 m, 4 m, and 3 m respectively.
The surface area of the cuboid = 2(lb + bh + lh) = 2(5×4 + 4×3 + 5×3) = 2(20 + 12 + 15) = 2 × 47 = 94 m²
Problem 2
What will be the surface area of a cuboid if its dimensions are 7 cm, 5 cm, and 2 cm?
We will find the surface area as 94 cm²
Explanation
For a cuboid with dimensions 7 cm, 5 cm, and 2 cm, the surface area is calculated as:
Surface Area = 2(lb + bh + lh) = 2(7×5 + 5×2 + 7×2) = 2(35 + 10 + 14) = 2 × 59 = 118 cm²
Problem 3
The surface area of a cuboid is 150 cm², and its dimensions are 5 cm, 3 cm, and h cm. Find the dimension h.
We find the height h as 4 cm
Explanation
To find the height, we use the formula Surface Area = 2(lb + bh + lh).
Here, the surface area is 150 cm², length is 5 cm, and breadth is 3 cm.
Substituting the values: 150 = 2(5×3 + 3×h + 5×h) 150 = 2(15 + 3h + 5h) 150 = 2(15 + 8h) 75 = 15 + 8h 60 = 8h h = 60/8 = 7.5 cm
Problem 4
Find the surface area of a cuboid with dimensions 8 m, 6 m, and 4 m.
We will find the surface area as 208 m²
Explanation
The given dimensions are 8 m, 6 m, and 4 m. The surface area of the cuboid is calculated using the formula:
Surface Area = 2(lb + bh + lh) = 2(8×6 + 6×4 + 8×4) = 2(48 + 24 + 32) = 2 × 104 = 208 m²
Problem 5
Help Lucy find the surface area of a cuboid if its length is 10 cm, breadth is 7 cm, and height is 3 cm.
We will find the surface area as 202 cm²
Explanation
The length is 10 cm, breadth is 7 cm, and height is 3 cm.
The surface area of the cuboid is:
Surface Area = 2(lb + bh + lh) = 2(10×7 + 7×3 + 10×3) = 2(70 + 21 + 30) = 2 × 121 = 242 cm²
FAQs on Surface Area of Cuboid
1.Is it possible for the surface area of a cuboid to be negative?
2.How to find the surface area of a cuboid if the dimensions are given?
3.How to find the surface area of a cuboid if only one dimension is given?
4.How is the volume of the cuboid calculated?
5.What is meant by the surface area of a cuboid?
Glossaries of Terms Related to Surface Area of Cuboid
- Surface Area: The total area that the surface of a three-dimensional object occupies.
- Cuboid: A three-dimensional shape with six rectangular faces, where opposite faces are equal.
- Rectangular Face: A flat surface with opposite sides equal and four right angles.
- Metric System: A system of measurement based on meters, liters, and grams.
- Imperial System: A system of measurement used primarily in the United States, including units such as inches, feet, and yards.
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
