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100 LearnersLast updated on September 4, 2025
Surface Area of Prism
A prism is a 3-dimensional shape that has two parallel, congruent bases connected by rectangular faces. The surface area of a prism is the total area covered by its outer surface. In this article, we will learn about the surface area of a prism.
What is the Surface Area of a Prism?
The surface area of a prism is the total area occupied by the boundary or surface of the prism. It is measured in square units.
A prism is a 3D shape with two identical bases and rectangular sides connecting the bases. Prisms can be classified into different types, such as rectangular prisms, triangular prisms, and more, depending on the shape of their bases.
The surface area of a prism includes the area of the bases and the lateral surface area, which is the area of the rectangular faces.
Surface Area of a Prism Formula
A prism has a lateral surface area and a total surface area. The lateral surface area refers to the sum of the areas of the rectangular faces, excluding the bases, while the total surface area includes the area of the bases as well.
Here is a general formula for calculating the surface area of a prism. For a prism with base perimeter P, base area B, and height h:
Lateral Surface Area = P × h
Total Surface Area = Lateral Surface Area + 2B
Lateral Surface Area of a Prism
The lateral surface area of a prism is the sum of the areas of all its side faces, excluding the bases.
For a prism with a base perimeter P and height h, the formula for the lateral surface area is:
Lateral Surface Area = P × h
Here, P is the perimeter of the base of the prism, and h is the height of the prism.
Total Surface Area of a Prism
The total surface area of a prism is the sum of the lateral surface area and the areas of the two bases. For a prism with base area B, base perimeter P, and height h, the formula for the total surface area is:
Total Surface Area = Lateral Surface Area + 2B
This can be rewritten as: Total Surface Area = P × h + 2B
Where B is the area of one base of the prism.
Volume of a Prism
The volume of a prism is the amount of space the prism occupies. It can be calculated by multiplying the area of the base by the height of the prism.
The formula for the volume of a prism is: Volume = B × h
Where B is the area of the base and h is the height of the prism.
Confusion between Lateral Surface Area and Total Surface Area
Students assume that the lateral surface area and the total surface area of a prism are the same. This confusion arises because both involve the height and base perimeter. Always remember that the lateral surface area includes only the rectangular faces, while the total surface area includes the bases as well.
Mistake 1
Using Only One Base Area for Total Surface Area
Some students mistakenly use only one base area when calculating the total surface area. Remember to include the areas of both bases in the formula for total surface area.
Mistake 2
Incorrect Calculation of Base Perimeter
A common mistake is incorrectly calculating the perimeter of the base, especially if the base is not a simple shape like a rectangle. Make sure to find the correct perimeter of the base shape.
Mistake 3
Using Height Instead of Base Dimensions
Some students mistakenly use the height of the prism instead of the dimensions of the base when calculating the base area. Always use the correct dimensions for the base.
Mistake 4
Assuming All Prisms Are Rectangular
Some students mistakenly believe that all prisms are rectangular, leading to incorrect calculations for bases that are non-rectangular. Prisms can have various base shapes, so use the correct formula for the shape of the base.
Mistake 5
Solved Examples of Surface Area of Prism
Find the lateral surface area of a triangular prism with a base perimeter of 12 cm and a height of 8 cm.
Lateral Surface Area = 96 cm²
Problem 1
Given P = 12 cm, h = 8 cm. Use the formula: Lateral Surface Area = P × h = 12 × 8 = 96 cm²
Find the total surface area of a rectangular prism with a base area of 20 cm², base perimeter of 18 cm, and height of 10 cm.
Explanation
Total Surface Area = 280 cm²
Problem 2
Use the formula: Total Surface Area = P × h + 2B = 18 × 10 + 2 × 20 = 180 + 40 = 220 cm²
A prism has a base area of 15 cm², a base perimeter of 14 cm, and a height of 6 cm. Find the total surface area.
Explanation
Total Surface Area = 144 cm²
Problem 3
Use the formula: Total Surface Area = P × h + 2B = 14 × 6 + 2 × 15 = 84 + 30 = 114 cm²
Find the lateral surface area of a prism with a base perimeter of 10 cm and a height of 12 cm.
Explanation
Lateral Surface Area = 120 cm²
Problem 4
Lateral Surface Area = P × h = 10 × 12 = 120 cm²
The height of a prism is 7 cm, and its lateral surface area is 154 cm². Find the base perimeter.
Explanation
Base Perimeter = 22 cm
It is the total area that covers the outside of the prism, including its rectangular faces and the two bases.
1.What are the two types of surface area in a prism?
2.How do you calculate the total surface area of a prism?
3.What is the formula for the lateral surface area of a prism?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Prism
Students often make mistakes while calculating the surface area of a prism, leading 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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