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146 LearnersLast updated on September 4, 2025
Surface Area of Rectangular Prism
A rectangular prism is a 3-dimensional shape with six rectangular faces. The surface area of the rectangular prism is the total area covered by its outer surface. In this article, we will learn about the surface area of a rectangular prism.
What is the Surface Area of a Rectangular Prism?
The surface area of a rectangular prism is the total area occupied by the surface of the prism. It is measured in square units.
A rectangular prism is a 3D shape with six faces, all of which are rectangles. It has opposite faces that are equal in area. In a rectangular prism, three dimensions are defined: length (l), width (w), and height (h).
Surface Area of a Rectangular Prism Formula
A rectangular prism has a total surface area composed of its six rectangular faces. The formula to find the total surface area (TSA) of a rectangular prism is:
Total Surface Area = 2(lw + lh + wh)
Where l is the length, w is the width, and h is the height of the rectangular prism.
Example Calculation for Surface Area of a Rectangular Prism
Consider a rectangular prism with a length of 5 cm, a width of 3 cm, and a height of 4 cm. The surface area can be calculated as follows:
Total Surface Area = 2(lw + lh + wh) = 2(5*3 + 5*4 + 3*4) = 2(15 + 20 + 12) = 2*47 = 94 cm²
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Volume of a Rectangular Prism
The volume of a rectangular prism shows how much space is inside it. It can be found using the formula: Volume = l*w*h It is measured in cubic units and represents the capacity of the prism.
Confusion between Surface Area and Volume
Students sometimes confuse the formulas for surface area and volume. Always remember that surface area is measured in square units and involves the area of all faces, while volume is measured in cubic units and involves multiplying all three dimensions.
Mistake 1
Incorrectly Calculating Face Areas
A common mistake is miscalculating the area of each face. Ensure each face's dimensions are used correctly in the formula for the total surface area.
Mistake 3
Using Incorrect Units
Always ensure that dimensions are in the same unit before performing calculations. The final surface area should be expressed in square units.
Mistake 4
Solved Examples of Surface Area of Rectangular Prism
Find the surface area of a rectangular prism with a length of 8 cm, a width of 5 cm, and a height of 2 cm.
Surface Area = 132 cmยฒ
Problem 1
Given l = 8 cm, w = 5 cm, h = 2 cm. Use the formula: TSA = 2(lw + lh + wh) = 2(8*5 + 8*2 + 5*2) = 2(40 + 16 + 10) = 2*66 = 132 cmยฒ
Find the surface area of a rectangular prism with dimensions 10 cm by 6 cm by 4 cm.
Explanation
Surface Area = 248 cm²
Problem 2
Use the formula: TSA = 2(lw + lh + wh) = 2(10*6 + 10*4 + 6*4) = 2(60 + 40 + 24) = 2*124 = 248 cmยฒ
A rectangular prism has a length of 7 cm, a width of 3 cm, and a height of 5 cm. Find the surface area.
Explanation
Surface Area = 142 cm²
It is the total area that covers the outside of a rectangular prism, including all six rectangular faces.
1.How do you calculate the surface area of a rectangular prism?
2.What unit is surface area measured in?
3.Can the surface area formula be used for other shapes?
4.Is surface area the same as volume?
Common Mistakes and How to Avoid Them in the Surface Area of a Rectangular Prism
Students often make mistakes while calculating the surface area of a rectangular prism, 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
