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104 LearnersLast updated on August 30, 2025
Surface Area of Isosceles Triangular Prism
An isosceles triangular prism is a 3-dimensional shape that has two parallel triangular bases and three rectangular lateral faces. The surface area of the isosceles triangular prism is the total area covered by its outer surface. The surface area includes the areas of the two triangular bases and the three rectangular lateral faces. In this article, we will learn about the surface area of an isosceles triangular prism.
What is the Surface Area of an Isosceles Triangular Prism?
The surface area of an isosceles triangular prism is the total area occupied by the boundary or surface of the prism.
It is measured in square units.
An isosceles triangular prism is a 3D shape with two identical triangular bases connected by three rectangular lateral faces.
The prism's surface area comprises the areas of both triangular bases and the three rectangular lateral faces.
Surface Area of an Isosceles Triangular Prism Formula
An isosceles triangular prism has two types of surface areas: the lateral surface area and the total surface area.
Consider the prism below to see its surface area, base width, height, and length.
An isosceles triangular prism has two types of surface areas:
Lateral Surface Area of an Isosceles Triangular Prism
Total Surface Area of an Isosceles Triangular Prism
Lateral Surface Area of an Isosceles Triangular Prism
The lateral surface area of an isosceles triangular prism is the area of the three rectangular faces, excluding the bases.
The formula for the lateral surface area (LSA) of the prism is given as:
Lateral Surface Area = perimeter of base × length
Here, the perimeter of the triangular base is the sum of its three sides.
Total Surface Area of an Isosceles Triangular Prism
The total area occupied by the isosceles triangular prism, including the areas of the triangular bases and the lateral faces, is known as the total surface area of the prism.
The total surface area is calculated using the formula: T
otal Surface Area = Lateral Surface Area + 2 × Base Area
Where the Base Area is the area of the triangular base of the prism.
Volume of an Isosceles Triangular Prism
The volume of an isosceles 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 the prism can be found using the formula: Volume = Base Area × length (cubic unit)
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 length and perimeter of the base.
Always remember that LSA is used on only the lateral faces, and TSA includes the lateral surface and the bases.
Mistake 1
Using incorrect base dimensions
Some students mistakenly use incorrect dimensions for the base when calculating the surface areas.
Ensure that you are using the correct dimensions of the triangular base for both perimeter and area calculations.
Mistake 2
Forgetting to include all faces in TSA
Students often calculate only the lateral surface and forget to add the area of the triangular bases.
Always include both parts when calculating the total surface area.
Total surface area = lateral surface area + 2 × base area.
Mistake 3
Incorrectly calculating the base area
A common mistake is using the wrong formula for the area of the triangular base. Remember to use the correct formula for the area of a triangle, especially when dealing with an isosceles triangle.
Mistake 4
Misinterpreting the prism's dimensions
Some students misinterpret the given dimensions, confusing height, base, or length. Always ensure that you understand which dimension corresponds to each part of the prism when performing calculations.
Mistake 5
Solved Examples of Surface Area of Isosceles Triangular Prism
Find the lateral surface area of an isosceles triangular prism with base perimeter 18 cm and length 10 cm.
LSA = 180 cm²
Problem 1
Given perimeter of base = 18 cm, length = 10 cm. Use the formula: LSA = perimeter of base × length = 18 × 10 = 180 cm²
Find the total surface area of an isosceles triangular prism with base area 25 cm², perimeter 20 cm, and length 12 cm.
Explanation
TSA = 290 cm²
Problem 2
Use the formula: TSA = Lateral Surface Area + 2 × Base Area LSA = perimeter of base × length = 20 × 12 = 240 cm² Base Area = 25 cm² TSA = 240 + 2 × 25 = 240 + 50 = 290 cm²
An isosceles triangular prism has a base area of 35 cm² and a length of 15 cm.
Find the total surface area if the perimeter of the base is 24 cm.
Explanation
TSA = 510 cm²
Problem 3
LSA = perimeter of base × length = 24 × 15 = 360 cm² Base Area = 35 cm² TSA = 360 + 2 × 35 = 360 + 70 = 430 cm²
Find the lateral surface area of an isosceles triangular prism with base perimeter 22 cm and length 8 cm.
Explanation
LSA = 176 cm²
Problem 4
LSA = perimeter of base × length = 22 × 8 = 176 cm²
The length of an isosceles triangular prism is 20 cm, and its lateral surface area is 240 cm².
Find the perimeter of the base.
Explanation
Perimeter = 12 cm
It is the total area that covers the outside of the prism, including its lateral faces and the bases.
1.What are the two types of surface area in an isosceles triangular prism?
2.What is the difference between base perimeter and base area?
3.Is the lateral surface area the same as 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 Isosceles Triangular Prism
Students often make mistakes while calculating the surface area of an isosceles triangular prism, which leads to wrong answers. Below are some common mistakes and 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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