Surface Area of Equilateral Triangular Prism
2026-02-28 10:36 Diff
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Last updated on August 5, 2025

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.

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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.

Problem 1

Given a = 5 cm, H = 12 cm. Use the formula: LSA = 3aH = 3 × 5 × 12 = 15 × 12 = 180 cm²

Okay, lets begin

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

Well explained 👍

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

Okay, lets begin

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

Well explained 👍

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

Okay, lets begin

Find the lateral surface area of an equilateral triangular prism with an edge length of 3 cm and a lateral height of 7 cm.

Well explained 👍

Problem 4

LSA = 3aH = 3 × 3 × 7 = 9 × 7 = 63 cm²

Okay, lets begin

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

Well explained 👍

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?

Lateral surface area and total surface area are the two types of surface area in an equilateral triangular prism.

2.What is the difference between edge length and lateral height?

Edge length is the length of the side of the equilateral triangle, while lateral height is the height of the prism.

3.Is the lateral surface area different from the total surface area?

Yes, the lateral surface area includes only the lateral faces, while the total surface area includes the bases as well.

4.What unit is surface area measured in?

Surface area is always measured in square units like cm², m², or in².

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.

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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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