Summarize this article:
103 LearnersLast updated on September 4, 2025
Surface Area of Right Rectangular Prism
A right rectangular prism is a 3-dimensional shape with six rectangular faces, where all angles are right angles. The surface area of a right rectangular prism is the total area covered by its outer surface. It includes the areas of all six faces. In this article, we will learn about the surface area of a right rectangular prism.
What is the Surface Area of a Right Rectangular Prism?
The surface area of a right rectangular prism is the total area occupied by the faces of the prism. It is measured in square units.
A right rectangular prism, also known as a cuboid, has two rectangular bases and four lateral rectangular faces. Its six faces are composed of three pairs of opposite rectangles.
The surface area is calculated by finding the area of each face and summing them all together.
Surface Area of a Right Rectangular Prism Formula
A right rectangular prism consists of six rectangular faces: two length by width, two width by height, and two height by length.
The total surface area is the sum of the areas of these faces. The formula for the total surface area (TSA) of a right rectangular prism is: Total Surface Area = 2lw + 2lh + 2wh
Where l is the length, w is the width, and h is the height of the prism.
Understanding the Surface Area Formula
The total surface area of a right rectangular prism accounts for all the faces of the prism. Each pair of opposite faces has the same area, which simplifies the calculation.
The formula is derived by adding up the areas of these pairs: TSA = 2(lw + lh + wh) This formula ensures that all six faces are included in the calculation.
Example Problem: Surface Area Calculation
To calculate the surface area of a right rectangular prism, measure the length, width, and height, then substitute these values into the formula.
For instance, if a prism has a length of 4 cm, a width of 3 cm, and a height of 5 cm, its surface area would be: TSA = 2(4 x 3 + 3 x 5 + 5 x 4) = 2(12 + 15 + 20) = 2(47) = 94 cm2
Volume of a Right Rectangular Prism
The volume of a right rectangular prism shows how much space is inside it. It is calculated by multiplying the length, width, and height of the prism:
Volume = l x w x h This formula tells us the capacity of the prism or how much it can hold.
Ignoring the Pairing of Opposite Faces
Students may forget that opposite faces are equal in area. This can lead to errors in calculating the total surface area. Always remember that each pair of opposite faces contributes twice their area.
Mistake 1
Confusing Volume with Surface Area
Some students mistakenly use volume formulas when calculating surface area. Remember, surface area involves adding up the areas of all faces, while volume is a product of dimensions.
Mistake 2
Incorrectly Adding Face Areas
A common mistake is to incorrectly compute or forget to double the areas of opposite faces. Double-check calculations for each face before combining them into the total surface area.
Mistake 3
Misidentifying Length, Width, and Height
Confusing these dimensions can lead to incorrect calculations. Always verify which dimension corresponds to length, width, and height based on context.
Mistake 4
Failure to Use Consistent Units
Ensure all measurements are in the same unit before calculating. Converting units incorrectly can lead to the wrong surface area measurement.
Mistake 5
Solved Examples of Surface Area of Right Rectangular Prism
Find the surface area of a right rectangular prism with length 8 cm, width 5 cm, and height 7 cm.
Surface Area = 262 cm²
Problem 1
Given l = 8 cm, w = 5 cm, h = 7 cm. Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(8 \times 5 + 5 \times 7 + 7 \times 8) = 2(40 + 35 + 56) = 2(131) = 262 \text{ cm}^2\)
Find the total surface area of a right rectangular prism with length 10 cm, width 4 cm, and height 6 cm.
Explanation
Surface Area = 248 cm²
Problem 2
Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(10 \times 4 + 4 \times 6 + 6 \times 10) = 2(40 + 24 + 60) = 2(124) = 248 \text{ cm}^2\)
A right rectangular prism has a length of 12 cm, a width of 7 cm, and a height of 9 cm. Find the surface area.
Explanation
Surface Area = 678 cm²
Problem 3
Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(12 \times 7 + 7 \times 9 + 9 \times 12) = 2(84 + 63 + 108) = 2(255) = 678 \text{ cm}^2\)
Calculate the surface area of a right rectangular prism with dimensions 3 cm, 4 cm, and 5 cm.
Explanation
Surface Area = 94 cm²
Problem 4
Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(3 \times 4 + 4 \times 5 + 5 \times 3) = 2(12 + 20 + 15) = 2(47) = 94 \text{ cm}^2\)
The surface area of a right rectangular prism is 214 cm². If its length is 7 cm and width is 5 cm, find its height.
Explanation
Height = 6 cm
It is the total area that covers the outside of the prism, including all its rectangular faces.
1.What is the formula for surface area of a right rectangular prism?
2.How do you differentiate surface area from volume?
3.Are the opposite faces of a right rectangular prism equal?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Right Rectangular Prism
Students often make mistakes while calculating the surface area of a right rectangular prism, leading to incorrect answers. Below are some common mistakes and ways to avoid them.
Explore More measurement
![Important Math Links Icon]()
Previous to Surface Area of Right Rectangular Prism
![Important Math Links Icon]()
Next to Surface Area of Right Rectangular Prism
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
