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137 LearnersLast updated on September 4, 2025
Surface Area of Triangular Prism
A triangular prism is a three-dimensional shape that has two identical triangular bases and three rectangular faces. The surface area of a triangular prism is the total area covered by its outer surface. This includes the areas of the two triangular bases and the three rectangular sides. In this article, we will learn about the surface area of a triangular prism.
What is the Surface Area of a Triangular Prism?
The surface area of a triangular prism is the total area occupied by the boundary or outer surface of the prism.It is measured in square units.
A triangular prism has two parallel triangular bases and three rectangular lateral surfaces.
Therefore, the surface area includes the areas of the two triangular bases and the three rectangles.
Triangular prisms can be right or oblique.A right triangular prism has rectangular lateral surfaces perpendicular to its bases, while an oblique triangular prism has lateral surfaces that are not perpendicular.
Surface Area of a Triangular Prism Formula
A triangular prism has two types of surface areas: the lateral surface area and the total surface area.Look at the triangular prism below to see its surface area, base area, and height.
A triangular prism has two types of surface areas:
- Lateral Surface Area of a Triangular Prism
- Total Surface Area of a Triangular Prism
Lateral Surface Area of a Triangular Prism
The lateral surface area of a triangular prism is the sum of the areas of its three rectangular sides.It does not include the area of the bases.
The formula for the LSA (Lateral Surface Area) of the triangular prism is given as:
Lateral Surface Area = perimeter of base × height
Here, the perimeter of the base is the sum of the sides of the triangular base.
The height is the perpendicular distance between the two triangular bases.
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Total Surface Area of a Triangular Prism
The total surface area of a triangular prism is the sum of the lateral surface area and the area of the two triangular bases. The formula for the total surface area is:
Total Surface Area = Lateral Surface Area + 2 × Base Area
Where the Base Area is the area of one triangular base.
Derivation of the Total Surface Area of a Triangular Prism
To find the total surface area, add the lateral area and twice the area of the base.
Consider a triangular prism with base area (B), height (h), and base perimeter (P).
Total surface area of a triangular prism = 2 × Base Area + Lateral Surface Area
Here, Base Area = area of one triangular base
Lateral Surface Area = perimeter of base × height
Volume of a Triangular Prism
The volume of a triangular prism shows how much space is inside it. It tells us the capacity of the prism.
The volume can be found using the formula: Volume = Base Area × height (cubic units)
Confusion between LSA and TSA
Students assume that the lateral surface area (LSA) and the total surface area (TSA) of a triangular prism are the same. Remember, LSA only includes the rectangular sides, while TSA includes both the lateral surface and the bases.
Mistake 1
Using height of the prism instead of height of the base
Some students mistakenly use the height of the prism instead of the height of the triangular base when finding the base area. Remember the formula for the area of a triangle is 1/2 × base × height, so always use the correct height.
Mistake 2
Incorrect calculation of the base perimeter
A common mistake is incorrectly calculating the perimeter of the triangular base. Ensure you add all three sides of the triangle to get the correct perimeter.
Mistake 3
Forgetting to include both bases in the total surface area
Students often calculate only the lateral surface and forget to add the areas of both triangular bases. Always include both bases when calculating the total surface area.
Mistake 4
Assuming lateral surface area and total surface area are different terms
Some students mistakenly believe lateral surface area and total surface area are the same, but they are different. The lateral surface area does not include the bases, while the total surface area includes both.
Mistake 5
Solved Examples of Surface Area of Triangular Prism
Find the lateral surface area of a triangular prism with base perimeter of 12 cm and height of 5 cm.
LSA = 60 cmยฒ
Problem 1
Given P = 12 cm, h = 5 cm. Use the formula: LSA = perimeter of base ร height = 12 ร 5 = 60 cmยฒ
Find the total surface area of a triangular prism with base area of 10 cm², base perimeter of 14 cm, and height of 6 cm.
Explanation
TSA = 104 cm²
Problem 2
Use the formula: TSA = 2 ร Base Area + Lateral Surface Area = 2 ร 10 + (14 ร 6) = 20 + 84 = 104 cmยฒ
A triangular prism has a base area of 15 cm², a base perimeter of 18 cm, and a height of 7 cm.
Find the total surface area.
Explanation
TSA = 156 cm²
Problem 3
Use the TSA formula: TSA = 2 ร Base Area + Lateral Surface Area = 2 ร 15 + (18 ร 7) = 30 + 126 = 156 cmยฒ
Find the lateral surface area of a triangular prism with a base perimeter of 20 cm and height of 8 cm.
Explanation
LSA = 160 cm²
Problem 4
LSA = perimeter of base ร height = 20 ร 8 = 160 cmยฒ
The height of a triangular prism is 10 cm, and its lateral surface area is 200 cm².
Find the base perimeter.
Explanation
Base perimeter = 20 cm
It is the total area that covers the outside of the prism, including its lateral surface and the bases.
1.What are the two types of surface area in a triangular prism?
2.How do you find the height of a triangular base?
3.Is lateral surface area the same as total surface area?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Triangular Prism
Students often make mistakes while calculating the surface area of a triangular prism, which leads to incorrect answers. Below are some common mistakes and the 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.
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