110 LearnersLast updated on August 5th, 2025
Surface Area of Box
A box, also known as a rectangular prism, is a 3-dimensional shape with six rectangular faces. The surface area of a box is the total area covered by its outer surface. In this article, we will learn about the surface area of a box.
What is the Surface Area of a Box?
The surface area of a box is the total area occupied by the boundary or surface of a box. It is measured in square units.
A box is a 3D shape with six faces, twelve edges, and eight vertices. Each face of a box is a rectangle, and opposite faces are equal. The surface area of a box includes the area of all six rectangular faces.
Surface Area of a Box Formula
A box has six rectangular faces, and the surface area is the sum of the areas of all these faces.
The formula for the surface area of a box with length (l), width (w), and height (h) is given as: Surface Area = 2(lw + lh + wh) square units
Calculating Surface Area of a Box
To calculate the surface area of a box, add up the areas of all six faces. The formula involves multiplying each pair of dimensions (length, width, and height) and then summing these products. Multiply the result by 2 to account for opposite faces being equal.
Surface Area = 2(lw + lh + wh)
Example Calculation of Surface Area
Consider a box with length 4 cm, width 3 cm, and height 5 cm.
Using the surface area formula: Surface Area = 2(lw + lh + wh) = 2(4×3 + 4×5 + 3×5) = 2(12 + 20 + 15) = 2×47 = 94 cm²
Volume of a Box
The volume of a box tells us how much space is inside it. The volume can be found by multiplying its length, width, and height.
The formula is: Volume = l × w × h cubic units
Forgetting to Multiply by 2
A common error is forgetting to multiply the sum of the face areas by 2, which accounts for both sets of opposite faces.
Ensure you use the complete formula: Surface Area = 2(lw + lh + wh).
Mistake 1
Incorrectly Identifying Dimensions
Sometimes students mix up length, width, and height. Clearly label each dimension to avoid confusion when calculating the surface area.
Mistake 2
Misplacing Parentheses
When applying the formula, ensure the addition inside the parentheses is completed before multiplying by 2. Follow the order of operations correctly.
Mistake 3
Using Inconsistent Units
Ensure all dimensions are in the same units before calculating. Convert them if necessary to avoid errors in the final result.
Mistake 4
Confusing Surface Area with Volume
Remember, surface area measures the external area of the box, while volume measures internal space. Use the correct formula for the calculation needed.
Mistake 5
Solved Examples of Surface Area of Box
Find the surface area of a box with dimensions 5 cm by 4 cm by 3 cm.
Surface Area = 94 cm²
Problem 1
Using the formula: Surface Area = 2(lw + lh + wh) = 2(5×4 + 5×3 + 4×3) = 2(20 + 15 + 12) = 2×47 = 94 cm²
Find the surface area of a box with dimensions 8 m by 6 m by 2 m.
Explanation
Surface Area = 112 m²
Problem 2
Using the formula: Surface Area = 2(lw + lh + wh) = 2(8×6 + 8×2 + 6×2) = 2(48 + 16 + 12) = 2×76 = 152 m²
A box has a length of 10 in, a width of 7 in, and a height of 4 in. Find the surface area.
Explanation
Surface Area = 268 in²
Problem 3
Using the formula: Surface Area = 2(lw + lh + wh) = 2(10×7 + 10×4 + 7×4) = 2(70 + 40 + 28) = 2×138 = 276 in²
Find the surface area of a box with dimensions 9 ft by 5 ft by 3 ft.
Explanation
Surface Area = 174 ft²
Problem 4
Using the formula: Surface Area = 2(lw + lh + wh) = 2(9×5 + 9×3 + 5×3) = 2(45 + 27 + 15) = 2×87 = 174 ft²
A box with dimensions 12 cm by 10 cm by 8 cm has a surface area of what?
Explanation
Surface Area = 592 cm²
It is the total area that covers the outside of the box, including all six rectangular faces.
1.How do you calculate the surface area of a box?
2.What units are used for surface area?
3.Is the surface area the same as the volume of a box?
4.Why do you multiply by 2 in the surface area formula?
Common Mistakes and How to Avoid Them in the Surface Area of a Box
Students often make mistakes while calculating the surface area of a box, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
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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.
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