105 LearnersLast updated on 30 August 2025
Surface Area of an Equilateral Triangular Prism
An equilateral triangular prism is a 3-dimensional shape with two congruent equilateral triangular bases and three rectangular lateral faces. The surface area of an equilateral triangular prism is the total area covered by its outer surface. The surface area includes the areas of both triangular bases and the 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 surface of the prism.
It is measured in square units. An equilateral triangular prism has two parallel equilateral triangles as its bases and three rectangular lateral faces.
Each side of the triangular base has the same length. To calculate the surface area, we consider both the areas of the triangular bases and the rectangular sides.
Surface Area of an Equilateral Triangular Prism Formula
An equilateral triangular prism has two types of surface areas: the area of its triangular bases and the area of its rectangular lateral faces.
Visualize the prism to understand its surface area, side length (s), and height (h).
The surface area of an equilateral triangular prism is given by:
Base Area of a Triangular Prism Lateral Surface Area of a Triangular Prism
Base Area of a Triangular Prism
The area of each triangular base is calculated using the formula for the area of an equilateral triangle.
The formula is: Base Area = (√3/4) × s² Here, s is the side length of the equilateral triangle.
Lateral Surface Area of a Triangular Prism
The lateral surface area is the total area of the three rectangular sides. It is calculated using the formula:
Lateral Surface Area = Perimeter of base × height = 3s × h
Where s is the side length of the triangular base, and h is the height of the prism.
Total Surface Area of an Equilateral Triangular Prism
The total surface area of the prism is the sum of the areas of the two triangular bases and the lateral surface area. It is calculated using the formula:
Total Surface Area = 2 × Base Area + Lateral Surface Area = 2 × (√3/4) × s² + 3s × h
Confusion between Base Area and Lateral Surface Area
Students may confuse the formulas for the base area and the lateral surface area. Remember that the base area is calculated using the formula for an equilateral triangle, while the lateral surface area involves the perimeter of the base and the height of the prism.
Mistake 1
Incorrect Calculation of Base Area
Some students might incorrectly calculate the base area by not using the correct formula for an equilateral triangle. Always use (√3/4) × s² for the area of each triangular base.
Mistake 2
Misusing the Perimeter in Lateral Surface Area
A common mistake is using only the side length instead of the perimeter in the lateral surface area formula. Use 3s for the perimeter of the base.
Mistake 3
Forgetting to Double the Base Area
Students might forget to multiply the base area by 2 when calculating the total surface area. Remember the total surface area includes both triangular bases.
Mistake 4
Assuming Different Formulas for Prisms
Some students may assume different surface area formulas for equilateral triangular prisms and other prisms, but the concept is the same. Ensure the correct formula is used for equilateral triangular prisms.
Mistake 5
Solved Examples of Surface Area of an Equilateral Triangular Prism
Find the surface area of an equilateral triangular prism with a side length of 6 cm and a height of 10 cm.
Surface Area = 197.94 cm²
Problem 1
Given s = 6 cm, h = 10 cm. Base Area of one triangle = (√3/4) × s² = (√3/4) × 36 = 9√3 cm² Lateral Surface Area = 3s × h = 3 × 6 × 10 = 180 cm² Total Surface Area = 2 × 9√3 + 180 ≈ 31.18 + 180 ≈ 211.18 cm²
Calculate the surface area of an equilateral triangular prism with side length 4 cm and height 8 cm.
Explanation
Surface Area = 105.86 cm²
Problem 2
Base Area of one triangle = (√3/4) × 4² = 4√3 cm² Lateral Surface Area = 3 × 4 × 8 = 96 cm² Total Surface Area = 2 × 4√3 + 96 ≈ 13.86 + 96 ≈ 109.86 cm²
An equilateral triangular prism has a side length of 5 cm and a height of 7 cm. Find its total surface area.
Explanation
Surface Area = 122.71 cm²
Problem 3
Base Area of one triangle = (√3/4) × 5² = 25√3/4 cm² Lateral Surface Area = 3 × 5 × 7 = 105 cm² Total Surface Area = 2 × (25√3/4) + 105 ≈ 21.65 + 105 ≈ 126.65 cm²
Find the surface area of an equilateral triangular prism where the side length is 3 cm and the height is 6 cm.
Explanation
Surface Area = 68.08 cm²
Problem 4
Base Area of one triangle = (√3/4) × 3² = (√3/4) × 9 = 2.25√3 cm² Lateral Surface Area = 3 × 3 × 6 = 54 cm² Total Surface Area = 2 × 2.25√3 + 54 ≈ 7.79 + 54 ≈ 61.79 cm²
Determine the surface area of an equilateral triangular prism with a side length of 8 cm and a height of 12 cm.
Explanation
Surface Area = 297.86 cm²
It is the total area that covers the outside of the prism, including both the triangular bases and the lateral rectangular faces.
1.What are the components of the surface area in an equilateral triangular prism?
2.How do you find the base area of an equilateral triangular prism?
3.What is the lateral surface area of an equilateral triangular prism?
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, leading to incorrect answers. Below are some common mistakes and 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
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