Summarize this article:
111 LearnersLast updated on August 30, 2025
Surface Area of a Triangular
A triangular is a 3-dimensional shape with a triangular base. The surface area of the triangular is the total area covered by its outer surface. The surface area of the triangular includes both its lateral faces and its base. In this article, we will learn about the surface area of a triangular.
What is the Surface Area of a Triangular?
The surface area of a triangular is the total area occupied by the boundary or surface of a triangular prism.
It is measured in square units.
A triangular prism is a 3D shape that has two parallel triangular bases and three rectangular faces connecting the corresponding sides of the two bases.
Thus, it has two types of surface areas: the lateral surface area, which includes only the three rectangular sides, and the total surface area, which includes both the lateral surface area and the two triangular bases.
Surface Area of a Triangular Prism Formula
A triangular prism has a lateral surface, and it has two types of surface areas: the lateral surface area and the total surface area.
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 area of the three rectangular sides of the triangular prism is known as the lateral surface area.
The formula for the LSA (Lateral Surface Area) of the triangular prism is given as:
Lateral Surface Area = perimeter of the base × height of the prism
Here, the perimeter of the base is the sum of the sides of the triangular base, and the height is the distance between the two triangular bases.
Total Surface Area of a Triangular Prism
The total area occupied by the triangular prism, including the area of the three lateral sides and the two triangular bases, is known as the total surface area of a triangular prism.
The total surface area of a triangular prism is calculated by using the formula:
Total surface area = Lateral Surface Area + 2 × Area of the triangular base
Where the area of the triangular base can be calculated using the formula: Area = 1/2 × base × height of the triangle.
Volume of a Triangular Prism
The volume of a triangular prism shows how much space is inside it. It tells us how much space is inside the prism or how much it can hold.
The volume of a triangular prism can be found by using the formula:
Volume = Area of the triangular base × height of the prism (cubic unit)
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.
This confusion arises because both involve the base perimeter and height of the prism.
Always remember that LSA is used for only the three lateral sides, and TSA includes the lateral surface and the two triangular bases.
Mistake 1
Incorrect calculation of base perimeter
Some students mistakenly use only one side of the triangular base instead of the perimeter when finding the lateral surface area. Remember the formula for lateral surface area requires the perimeter of the triangular base.
Mistake 2
Forgetting to include both triangular bases in the total surface area
Students often calculate only the lateral surface and forget to add both triangular bases. Always include both parts when calculating the total surface area. Total surface area = lateral surface area + 2 × area of the triangular base.
Mistake 3
Using the wrong formula for the area of the triangular base
A common mistake is using the wrong formula for calculating the area of the triangular base. Always use the formula: Area = 1/2 × base × height of the triangle.
Mistake 4
Assuming lateral surface area and total surface area are different for each shape
Some students believe that the lateral surface area and total surface area concepts are different for each shape. However, the principle of combining lateral and base areas applies to all prisms.
Mistake 5
Solved Examples of Surface Area of a Triangular Prism
Find the lateral surface area of a triangular prism with a base perimeter of 12 cm and a height of 8 cm.
LSA = 96 cm²
Problem 1
Given the base perimeter = 12 cm, height = 8 cm. Use the formula: LSA = perimeter of the base × height = 12 × 8 = 96 cm²
Find the total surface area of a triangular prism with a base area of 15 cm², base perimeter of 10 cm, and height of 6 cm.
Explanation
TSA = 90 cm²
Problem 2
Use the formula: TSA = LSA + 2 × area of the triangular base LSA = perimeter of the base × height = 10 × 6 = 60 cm² TSA = 60 + 2 × 15 = 60 + 30 = 90 cm²
A triangular prism has a base perimeter of 18 cm and a height of 10 cm. Find the lateral surface area.
Explanation
LSA = 180 cm²
Problem 3
Use the formula: LSA = perimeter of the base × height = 18 × 10 = 180 cm²
Find the total surface area of a triangular prism with a base perimeter of 14 cm, base area of 20 cm², and height of 12 cm.
Explanation
TSA = 148 cm²
Problem 4
Use the formula: TSA = LSA + 2 × area of the triangular base LSA = perimeter of the base × height = 14 × 12 = 168 cm² TSA = 168 + 2 × 20 = 168 + 40 = 208 cm²
The height of a triangular prism is 9 cm, and its lateral surface area is 108 cm². Find the base perimeter.
Explanation
Base perimeter = 12 cm
It is the total area that covers the outside of the triangular prism, including its three lateral sides and the two triangular bases.
1.What are the two types of surface area in a triangular prism?
2.How is the lateral surface area of a triangular prism calculated?
3.Is the concept of lateral surface area and total surface area different for each shape?
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 wrong answers. Below are some common mistakes and the ways to avoid them.
Explore More measurement
![Important Math Links Icon]()
Previous to Surface Area of a Triangular
![Important Math Links Icon]()
Next to Surface Area of a Triangular
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
