Surface Area of a Triangular
2026-02-28 09:46 Diff
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Last updated on August 30, 2025

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.

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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.

Problem 1

Given the base perimeter = 12 cm, height = 8 cm. Use the formula: LSA = perimeter of the base × height = 12 × 8 = 96 cm²

Okay, lets begin

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.

Well explained 👍

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

Okay, lets begin

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

Well explained 👍

Problem 3

Use the formula: LSA = perimeter of the base × height = 18 × 10 = 180 cm²

Okay, lets begin

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

Well explained 👍

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

Okay, lets begin

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

Well explained 👍

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?

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

2.How is the lateral surface area of a triangular prism calculated?

The lateral surface area is calculated by multiplying the perimeter of the triangular base by the height of the prism.

3.Is the concept of lateral surface area and total surface area different for each shape?

No, the principle of combining lateral and base areas applies universally to prisms and similar shapes.

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 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.

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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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