102 LearnersLast updated on 30 August 2025
Surface Area of 3D Rectangle
A 3D rectangle, also known as a rectangular prism or cuboid, is a 3-dimensional shape with six rectangular faces. The surface area of a 3D rectangle is the total area covered by its outer surface. It includes the areas of all six faces of the cuboid. In this article, we will learn about the surface area of a 3D rectangle.
What is the Surface Area of a 3D Rectangle?
The surface area of a 3D rectangle is the total area occupied by its external surfaces. It is measured in square units.
A 3D rectangle has six rectangular faces, forming a box-like shape.
Each face has a length and width, and the total surface area is the sum of the areas of all these faces.
Cuboids are often found in everyday objects like boxes, bricks, and books.
Surface Area of a 3D Rectangle Formula
A 3D rectangle has six faces, and the surface area is calculated by adding the areas of all these faces.
They are paired as opposite faces, each having the same area.
A cuboid has three pairs of opposite faces. If the dimensions are given as length (l), width (w), and height (h), the formula for the surface area is: Surface Area = 2(lw + lh + wh)
Finding the Surface Area of a 3D Rectangle
To calculate the surface area of a 3D rectangle, you must find the area of each pair of opposite faces and then add them up.
The formula is derived from adding the areas of the three unique faces and multiplying by two:
Surface Area = 2(lw + lh + wh)
Here, l is the length, w is the width, and h is the height of the cuboid.
Example Calculations of Surface Area
Let's use an example to better understand the calculation. Consider a 3D rectangle with dimensions:
Length = 4 cm
Width = 3 cm
Height = 5 cm
Using the 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 3D Rectangle
The volume of a 3D rectangle indicates how much space it occupies.
It is calculated using the product of its dimensions: length, width, and height.
The formula for the volume is: Volume = l×w×h (cubic units)
Mixing Up Dimensions
Students may confuse length, width, and height. Always ensure you correctly label and use these dimensions in the formula.
Mistake 1
Omitting Pairs of Faces
Some students forget to account for all six faces of the cuboid. Remember to calculate the area of each pair of opposite faces and add them together.
Mistake 2
Misapplying the Formula
Another common mistake is incorrectly applying the formula. Verify that all terms in the formula are multiplied and added properly: Surface Area = 2(lw + lh + wh).
Mistake 3
Calculation Errors
Errors in arithmetic calculations can lead to wrong answers. Double-check your math, especially when multiplying and adding areas.
Mistake 4
Confusing Surface Area and Volume
Some students confuse surface area with volume. Remember, surface area measures the outer surface, while volume measures the space inside.
Mistake 5
Solved Examples of Surface Area of 3D Rectangle
Find the surface area of a 3D rectangle with length 6 cm, width 4 cm, and height 3 cm.
Surface Area = 108 cm²
Problem 1
Given l = 6 cm, w = 4 cm, h = 3 cm. Use the formula: Surface Area = 2(lw + lh + wh) = 2(6×4 + 6×3 + 4×3) = 2(24 + 18 + 12) = 2×54 = 108 cm²
Find the surface area of a 3D rectangle with dimensions: length 8 cm, width 5 cm, and height 7 cm.
Explanation
Surface Area = 262 cm²
Problem 2
Use the formula: Surface Area = 2(lw + lh + wh) = 2(8×5 + 8×7 + 5×7) = 2(40 + 56 + 35) = 2×131 = 262 cm²
A box has dimensions of length 10 cm, width 6 cm, and height 4 cm. Find the surface area.
Explanation
Surface Area = 248 cm²
Problem 3
Use the formula: Surface Area = 2(lw + lh + wh) = 2(10×6 + 10×4 + 6×4) = 2(60 + 40 + 24) = 2×124 = 248 cm²
Calculate the surface area of a rectangular prism with length 9 cm, width 3 cm, and height 5 cm.
Explanation
Surface Area = 174 cm²
Problem 4
Surface Area = 2(lw + lh + wh) = 2(9×3 + 9×5 + 3×5) = 2(27 + 45 + 15) = 2×87 = 174 cm²
The surface area of a 3D rectangle is 150 cm². If its length and width are 5 cm and 3 cm, respectively, find the height.
Explanation
Height = 5 cm
It is the total area that covers the outside of the 3D rectangle, including all its six rectangular faces.
1.How do you calculate the surface area of a 3D rectangle?
2.What is the difference between surface area and volume?
3.Can surface area be measured in cubic units?
4.Are all sides of a 3D rectangle equal?
Common Mistakes and How to Avoid Them in the Surface Area of a 3D Rectangle
Students often make mistakes while calculating the surface area of a 3D rectangle, leading to incorrect answers. Below are some common mistakes and ways to avoid them.
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
