104 LearnersLast updated on August 29, 2025
Surface Area of the Right Triangular Prism
A right triangular prism is a 3-dimensional shape with two triangular bases and three rectangular lateral faces. The surface area of a right triangular prism is the total area covered by its outer surface. It includes the area of the two triangular bases and the three rectangular lateral faces. In this article, we will learn about the surface area of a right triangular prism.
What is the Surface Area of a Right Triangular Prism?
The surface area of a right triangular prism is the total area occupied by the boundary or surface of the prism. It is measured in square units. A right triangular prism is a 3D shape that has two parallel triangular bases connected by three rectangular faces.
It has two triangular faces and three rectangular faces. The surface area includes both the lateral surface area and the base area. Right triangular prisms have their triangular faces aligned directly above each other, forming a neat shape.
Surface Area of a Right Triangular Prism Formula
A right triangular prism has three lateral faces, which are rectangles, and two bases, which are triangles.
To find the surface area, you need to calculate the area of these faces and then sum them up.
The formula for the surface area of a right triangular prism is: Surface Area = Lateral Surface Area + 2 × Base Area
Lateral Surface Area of a Right Triangular Prism
The lateral surface area of a right triangular prism refers to the sum of the areas of the three rectangular faces.
If the sides of the triangular base are a, b, and c, and the height of the prism is h, the formula for the lateral surface area (LSA) is:
Lateral Surface Area = (a + b + c) × h square units
Here, a, b, and c are the lengths of the sides of the triangular base, and h is the height of the prism.
Total Surface Area of a Right Triangular Prism
The total surface area of a right triangular prism is the sum of the lateral surface area and the areas of the two triangular bases. The formula is:
Total Surface Area = Lateral Surface Area + 2 × Base Area Base Area = ½ × base × height of the triangle
Volume of a Right Triangular Prism
The volume of a right triangular prism shows how much space is inside it. It is calculated by using the formula:
Volume = Base Area × Height of the Prism = ½ × base × height of the triangle × height of the prism
Ignoring the Triangular Base Areas
Students sometimes forget to include the areas of the two triangular bases while calculating the total surface area. Always remember that the total surface area includes both the lateral surface area and twice the area of the base.
Mistake 1
Confusing the Height of the Prism with the Height of the Triangle
Students often confuse the height of the prism with the height of the triangular base. Remember that the height of the prism is the perpendicular distance between the two triangular bases, while the height of the triangle is used to calculate the base area.
Mistake 2
Using Incorrect Formula for Base Area
A common mistake is using an incorrect formula for the area of the triangular base. Always use the formula: Base Area = ½ × base × height of the triangle.
Mistake 3
Misplacing Measurements
Students often mix up the measurements of the sides of the triangle or the height of the prism. Always double-check the dimensions before substituting them into the formulas.
Mistake 4
Overlooking the Need for All Dimensions
Some students forget that all side lengths of the triangular base and the height of the prism are needed to calculate the surface area accurately. Ensure you have all necessary dimensions before starting calculations.
Mistake 5
Solved Examples of Surface Area of a Right Triangular Prism
Find the lateral surface area of a right triangular prism with base sides 3 cm, 4 cm, and 5 cm, and a height of 10 cm.
LSA = 120 cm²
Problem 1
Given a = 3 cm, b = 4 cm, c = 5 cm, and h = 10 cm. Use the formula: LSA = (a + b + c) × h = (3 + 4 + 5) × 10 = 12 × 10 = 120 cm²
Find the total surface area of a right triangular prism with base sides 6 cm, 8 cm, and 10 cm, and a height of 15 cm.
Explanation
TSA = 396 cm²
Problem 2
Use the formula: TSA = Lateral Surface Area + 2 × Base Area Base Area = ½ × base × height of the triangle = ½ × 6 × 8 = 24 cm² LSA = (6 + 8 + 10) × 15 = 360 cm² TSA = 360 + 2 × 24 = 408 cm²
A right triangular prism has base sides of 5 cm, 12 cm, and 13 cm, with a height of 20 cm. Find the total surface area.
Explanation
TSA = 740 cm²
Problem 3
Find the base area using: Base Area = ½ × base × height of the triangle = ½ × 5 × 12 = 30 cm² LSA = (5 + 12 + 13) × 20 = 600 cm² TSA = 600 + 2 × 30 = 660 cm²
Find the lateral surface area of a right triangular prism with base sides 7 cm, 24 cm, and 25 cm, and a height of 18 cm.
Explanation
LSA = 1008 cm²
Problem 4
LSA = (7 + 24 + 25) × 18 = 56 × 18 = 1008 cm²
The lateral surface area of a right triangular prism is 330 cm², and the height is 10 cm. If the perimeter of the triangular base is 33 cm, find the height of the prism.
Explanation
Height = 10 cm
It is the total area that covers the outside of the right triangular prism, including its lateral faces and the two triangular bases.
1.What are the two main components of the surface area in a right triangular prism?
2.What is the difference between the height of the prism and the height of the triangle?
3.How is the base area of a triangular prism calculated?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Right Triangular Prism
Students often make mistakes while calculating the surface area of a right triangular prism, leading 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.
Fun Fact
: She has songs for each table which helps her to remember the tables
