101 LearnersLast updated on August 5th, 2025
Surface Area of Rectangular Box
A rectangular box is a three-dimensional shape with six rectangular faces. The surface area of a rectangular box is the total area covered by its outer surfaces. It includes the areas of all its faces. In this article, we will learn about the surface area of a rectangular box.
What is the Surface Area of a Rectangular Box?
The surface area of a rectangular box is the total area occupied by the boundary or surface of the box. It is measured in square units.
A rectangular box is a 3D shape with six rectangular faces, where opposite faces are equal in area. Each face is a rectangle, which contributes to the total surface area.
To find the surface area, we calculate the area of each face and add them together.
Surface Area of a Rectangular Box Formula
A rectangular box has six faces, and the total surface area is the sum of the areas of these faces. Look at the box below to understand its surface area, length(l), width(w), and height(h).
A rectangular box has three pairs of opposite faces:
Two faces with dimensions l × w
Two faces with dimensions w × h
Two faces with dimensions h × l
The formula for the total surface area is: Surface Area = 2(lw + wh + hl) square units
Calculating the Surface Area of a Rectangular Box
To find the surface area of a rectangular box, calculate the area of each pair of opposite faces and then sum them up. The formula can be broken down as follows: -
Area of the top and bottom faces = 2 × (length × width)
Area of the front and back faces = 2 × (width × height)
Area of the left and right faces = 2 × (height × length)
Add these areas to get the total surface area: Surface Area = 2(lw + wh + hl)
Example Calculations
Let's consider a rectangular box with specific dimensions and calculate its surface area using the formula. Example: Find the surface area of a box with length 5 cm, width 3 cm, and height 4 cm.
Surface Area = 2(lw + wh + hl) = 2(5 × 3 + 3 × 4 + 4 × 5) = 2(15 + 12 + 20) = 2(47) = 94 cm²
Volume of a Rectangular Box
The volume of a rectangular box indicates the amount of space it occupies. It is calculated by multiplying its length, width, and height.
The formula for the volume of a rectangular box is: Volume = l × w × h cubic units
Confusing Surface Area with Volume
Students sometimes confuse surface area with volume. Remember, surface area is the total area of all sides, while volume is the space inside the box.
Mistake 1
Forgetting to Multiply by 2
A common mistake is forgetting to multiply the sum of the areas of the three different pairs of faces by 2. Always ensure you double the sum to account for both pairs of opposite faces.
Mistake 2
Incorrectly Assigning Dimensions
Students may mix up the dimensions of the box, using the wrong values for length, width, or height. Always verify that each dimension is correctly identified before performing calculations.
Mistake 3
Using Incorrect Units
Ensure that the dimensions are in the same units before substituting them into the formula. Surface area is measured in square units, so check that dimensions are consistent.
Mistake 4
Neglecting One Pair of Faces
Sometimes students forget to include one pair of opposite faces in their calculations. Remember that a rectangular box has three pairs of opposite faces, each contributing to the total surface area.
Mistake 5
Solved Examples of Surface Area of Rectangular Box
Find the surface area of a rectangular box with a length of 8 cm, width of 6 cm, and height of 5 cm.
Surface Area = 236 cm²
Problem 1
Use the formula: Surface Area = 2(lw + wh + hl) = 2(8 × 6 + 6 × 5 + 5 × 8) = 2(48 + 30 + 40) = 2(118) = 236 cm²
Find the surface area of a rectangular box with length 10 cm, width 4 cm, and height 7 cm.
Explanation
Surface Area = 268 cm²
Problem 2
Use the formula: Surface Area = 2(lw + wh + hl) = 2(10 × 4 + 4 × 7 + 7 × 10) = 2(40 + 28 + 70) = 2(138) = 276 cm²
A rectangular box has a length of 9 cm, width of 5 cm, and height of 2 cm. Find the surface area.
Explanation
Surface Area = 148 cm²
Problem 3
Use the formula: Surface Area = 2(lw + wh + hl) = 2(9 × 5 + 5 × 2 + 2 × 9) = 2(45 + 10 + 18) = 2(73) = 146 cm²
Find the surface area of a box with length 12 cm, width 7 cm, and height 3 cm.
Explanation
Surface Area = 282 cm²
Problem 4
Use the formula: Surface Area = 2(lw + wh + hl) = 2(12 × 7 + 7 × 3 + 3 × 12) = 2(84 + 21 + 36) = 2(141) = 282 cm²
The width of a rectangular box is 6 cm, its height is 4 cm, and its surface area is 208 cm². Find the length.
Explanation
Length = 10 cm
It is the total area that covers the outside of the box, including all six rectangular faces.
1.What dimensions are needed to calculate the surface area of a rectangular box?
2.How do you differentiate between surface area and volume?
3.What is the formula for the surface area of a rectangular box?
4.In what units is surface area measured?
Common Mistakes and How to Avoid Them in the Surface Area of a Rectangular Box
Students often make mistakes while calculating the surface area of a rectangular box, which leads to incorrect answers. Below are some common mistakes and ways to avoid them.
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Seyed Ali Fathima S
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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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