100 LearnersLast updated on July 31st, 2025
Surface Area of Equilateral Triangular Prism
An equilateral triangular prism is a 3-dimensional shape with two parallel triangular bases that are equilateral triangles. The surface area of an equilateral triangular prism is the total area covered by its outer surfaces. It includes the areas of its triangular bases and the three rectangular lateral faces. In this article, we will learn about the surface area of an equilateral triangular prism.
What is the Surface Area of an Equilateral Triangular Prism?
The surface area of an equilateral triangular prism is the total area occupied by the boundary or surface of the prism. It is measured in square units.
An equilateral triangular prism consists of two parallel equilateral triangles and three rectangular lateral faces. The surface area of the prism includes the areas of the two triangular bases and the lateral surfaces.
Surface Area of an Equilateral Triangular Prism Formula
An equilateral triangular prism has two types of surface areas: the lateral surface area and the total surface area. Look at the prism below to understand its surface area, height (h), edge length (a), and the lateral height (H).
An equilateral triangular prism has two types of surface areas:
Lateral Surface Area of an Equilateral Triangular Prism
Total Surface Area of an Equilateral Triangular Prism
Lateral Surface Area of an Equilateral Triangular Prism
The lateral surface area of an equilateral triangular prism is the sum of the areas of the three rectangular lateral faces. The formula for the LSA (Lateral Surface Area) of the prism is given as: Lateral Surface Area = 3aH square units Here, a is the edge length of the equilateral triangle, and H is the lateral height of the prism.
Total Surface Area of an Equilateral Triangular Prism
The total surface area of an equilateral triangular prism is the sum of the lateral surface area and the areas of the two triangular bases.
The formula for the total surface area is: Total Surface Area = Lateral Surface Area + 2 × Area of the Base
The area of each triangular base is given by the formula: Area of the Base = (√3/4) × a²
Substituting these into the total surface area, Total Surface Area = 3aH + 2 × (√3/4) × a²
Volume of an Equilateral Triangular Prism
The volume of an equilateral triangular prism shows how much space is inside it. It can be found using the formula:
Volume = (Base Area) × Height = (√3/4) × a² × H cubic units
Confusion between LSA and TSA
Students assume that the lateral surface area (LSA) and the total surface area (TSA) of a prism are the same. This confusion arises because both involve the side lengths and height. Always remember that LSA includes only the lateral surfaces, while TSA also includes the bases.
Mistake 1
Using incorrect base area formula
Some students mistakenly use the wrong formula for the area of the triangular base. Remember the formula for an equilateral triangle's area: (√3/4) × a².
Mistake 2
Using the wrong height for lateral surface area
A common mistake is using the height of the triangle instead of the lateral height when finding the lateral surface area. Use the prism's height (H) for lateral surface calculations.
Mistake 3
Forgetting to include both bases in the total surface area
Students often calculate only one triangular base instead of both. Always include both bases when calculating the total surface area.
Mistake 4
Confusion between edge length and lateral height
Some students mistakenly interchange the edge length of the triangle (a) and the lateral height (H). Ensure you know which measurement corresponds to the triangle's edge and which is the height of the prism.
Mistake 5
Solved Examples of Surface Area of Equilateral Triangular Prism
Find the lateral surface area of an equilateral triangular prism with an edge length of 5 cm and a lateral height of 12 cm.
LSA = 180 cm²
Problem 1
Given a = 5 cm, H = 12 cm. Use the formula: LSA = 3aH = 3 × 5 × 12 = 15 × 12 = 180 cm²
Find the total surface area of an equilateral triangular prism with an edge length of 4 cm and a lateral height of 10 cm.
Explanation
TSA = 125.86 cm²
Problem 2
Use the formula: TSA = 3aH + 2 × (√3/4) × a² = 3 × 4 × 10 + 2 × (√3/4) × 4² = 120 + 2 × (√3/4) × 16 = 120 + 2 × 6.928 = 120 + 13.856 = 133.856 cm²
An equilateral triangular prism has an edge length of 6 cm and a lateral height of 8 cm. Find the total surface area.
Explanation
TSA = 204.78 cm²
Problem 3
Use the formula: TSA = 3aH + 2 × (√3/4) × a² = 3 × 6 × 8 + 2 × (√3/4) × 6² = 144 + 2 × (√3/4) × 36 = 144 + 2 × 15.588 = 144 + 31.176 = 175.176 cm²
Find the lateral surface area of an equilateral triangular prism with an edge length of 3 cm and a lateral height of 7 cm.
Explanation
LSA = 63 cm²
Problem 4
LSA = 3aH = 3 × 3 × 7 = 9 × 7 = 63 cm²
The lateral height of an equilateral triangular prism is 15 cm, and its lateral surface area is 225 cm². Find the edge length.
Explanation
Edge length = 5 cm
It is the total area that covers the outside of the prism, including its lateral surfaces and the two triangular bases.
1.What are the two types of surface area in an equilateral triangular prism?
2.What is the difference between edge length and lateral height?
3.Is the lateral surface area different from the total surface area?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of an Equilateral Triangular Prism
Students often make mistakes while calculating the surface area of an equilateral triangular prism, which leads to wrong 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
