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130 LearnersLast updated on December 11, 2025
Lateral Surface Area of an Equilateral Triangular Prism
An equilateral triangular prism consists of two triangular bases and three rectangular lateral surfaces. The lateral surface area represents the sum of the areas of these rectangular surfaces. Let's take an example of a Toblerone chocolate box, where the triangular sides are the bases, and the rectangular sides form the lateral surface area of the prism.
What is the 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 faces formed between the two triangular bases.
Formula for Lateral Surface Area of an Equilateral Triangular Prism
How to Find Lateral Surface Area of an Equilateral Triangular Prism
To find the Lateral Surface Area of an Equilateral Triangular Prism, follow these steps:
Step 1: Note the given parameters, such as the side length of the triangular base and the height of the prism.
Step 2: Ensure all measurements are in the same unit before calculation.
Step 3: Use the equation, Area = 3ah, to find the LSA of the prism.
Step 4: Provide the calculated answer in square units.
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Common mistakes and how to avoid them in the Lateral Surface Area of an Equilateral Triangular Prism.
There are a few typical mistakes people make while calculating the lateral surface area of an equilateral triangular prism.
Some of them are listed below:
Mistake 1
Using incorrect side lengths for the base.
A common mistake is assuming different side lengths for the equilateral triangle base, while all sides should be equal.
Mistake 2
Miscalculating the perimeter of the triangular base.
Ensure that the perimeter used in the formula is calculated as P = 3a, where "a" is the side length of the triangular base.
Mistake 3
Not mentioning the units with the numerical value.
It's important to mention the unit with the answer, even if the question doesn't specify the unit.
It's preferable to write “square units” as a unit for the standard representation of a value.
Mistake 5
Confusing lateral surface area with the total surface area.
Lateral surface area is the sum of the areas of the rectangular sides only, while total surface area includes the area of the triangular bases as well.
Solved examples on Lateral Surface Area of an Equilateral Triangular Prism
Problem 1
What is the lateral area of an equilateral triangular prism with a base side length of 5 cm and a height of 10 cm?
150 cm²
Explanation
Given: Side length of base = 5 cm, Height of prism = 10 cm
LSA = 3ah = 3×5×10 = 150 cm²
Problem 2
Calculate the lateral surface area of an equilateral triangular prism having a base side length of 4 cm and a height of 7 cm.
84 cm²
Explanation
Given: Side length of base = 4 cm, Height of prism = 7 cm
LSA = 3ah = 3×4×7 = 84 cm²
Problem 3
If the lateral surface area of an equilateral triangular prism is 120 cmยฒ and the height is 8 cm, find the side length of the base.
5 cm
Explanation
Given: LSA = 120 cm², Height = 8 cm
Formula: LSA = 3ah
120 = 3×a×8
a = 120/24 = 5 cm
Problem 4
Evaluate the height of an equilateral triangular prism if its base side length is 6 units and its lateral surface area is 180 square units.
10 units
Explanation
Given: Side length of base = 6 units, LSA = 180 square units
Formula: LSA = 3ah
180 = 3×6×h
h = 180/18 = 10 units
Problem 5
The lateral surface area of an equilateral triangular prism is 90 cmยฒ. If its base side length is 3 cm, find its height.
10 cm
Explanation
Given: LSA = 90 cm², Side length of base = 3 cm
Formula: LSA = 3ah
90 = 3×3×h
h = 90/9 = 10 cm
FAQโs on Lateral Surface Area
1.What is Lateral Surface Area?
2.How to calculate the lateral surface area?
3.Is the lateral surface area and the total surface area the same?
4.What is the relation between the perimeter of the base and its side length?
5.How does the LSA change if the side length is doubled?
Important Glossary for Lateral Surface Area
- Equilateral Triangle: A triangle with all three sides of equal length.
- Prism: A solid geometric figure with two identical ends and flat sides.
- Perimeter: The total length around a two-dimensional shape.
- Lateral Surface Area: The sum of the areas of all the side faces of a three-dimensional object, excluding the base(s).
- Height of a Prism: The perpendicular distance between the two bases of the prism.
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
