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107 LearnersLast updated on August 30, 2025
Surface Area of Equilateral Triangular Pyramid
An equilateral triangular pyramid is a 3-dimensional shape with four equilateral triangular faces. The surface area of this pyramid is the total area covered by its outer surface. In this article, we will learn about the surface area of an equilateral triangular pyramid.
What is the Surface Area of an Equilateral Triangular Pyramid?
The surface area of an equilateral triangular pyramid is the total area occupied by the boundary or surface of the pyramid.
It is measured in square units.
An equilateral triangular pyramid, also known as a tetrahedron, is a 3D shape with four faces, all of which are equilateral triangles.
It does not have a curved surface like a cone but consists entirely of flat triangular faces.
The surface area of an equilateral triangular pyramid includes all its triangular faces.
Surface Area of an Equilateral Triangular Pyramid Formula
An equilateral triangular pyramid has four triangular faces. Its surface area is calculated by summing the areas of all these faces
. If each edge of the pyramid has length a, the formula for the surface area is:
Surface Area = 4 × (√3/4) × a²
This formula comes from the area of an equilateral triangle, which is (√3/4) × a², multiplied by the four faces of the pyramid.
Area of an Equilateral Triangle
The area of one equilateral triangular face of the pyramid is calculated using the formula for the area of an equilateral triangle:
Area = (√3/4) × a² where a is the length of a side of the equilateral triangle.
Total Surface Area of an Equilateral Triangular Pyramid
The total surface area of the equilateral triangular pyramid is the sum of the areas of its four triangular faces.
Using the formula:
Total Surface Area = 4 × (√3/4) × a² This results in: Total Surface Area = √3 × a²
Volume of an Equilateral Triangular Pyramid
The volume of an equilateral triangular pyramid shows how much space is inside it.
The formula for the volume of a tetrahedron (equilateral triangular pyramid) is:
Volume = (a³√2) / 12 where a is the length of an edge.
Confusion between Surface Area and Volume
Students may confuse the formula for surface area with that for volume. Remember that surface area is concerned with the outer surfaces, while volume measures the space inside.
Mistake 1
Using the Wrong Formula for Triangle Area
Some students use the wrong formula for the area of an equilateral triangle. Always use (√3/4) × a² for an equilateral triangle.
Mistake 2
Misidentifying Edge Length
Ensure that all edges are equal in an equilateral triangular pyramid. Using different lengths will lead to errors in calculations.
Mistake 3
Incorrect Calculation of Square Root
Errors can occur when calculating the square root of 3. Use an accurate value for √3, such as 1.732, to ensure precision.
Mistake 4
Forgetting to Multiply by Four
Students may forget to multiply by four for the surface area, as it accounts for all four triangular faces of the pyramid.
Mistake 5
Solved Examples of Surface Area of Equilateral Triangular Pyramid
Find the surface area of an equilateral triangular pyramid with each edge measuring 6 cm.
Surface Area = 62.35 cm²
Problem 1
Given a = 6 cm. Use the formula: Surface Area = √3 × a² = 1.732 × 6² = 1.732 × 36 = 62.352 cm²
Find the surface area of an equilateral triangular pyramid with edge length 4 cm.
Explanation
Surface Area = 27.71 cm²
Problem 2
Use the formula: Surface Area = √3 × a² = 1.732 × 4² = 1.732 × 16 = 27.712 cm²
An equilateral triangular pyramid has an edge length of 5 cm. Find its total surface area.
Explanation
Surface Area = 43.30 cm²
Problem 3
Use the formula: Surface Area = √3 × a² = 1.732 × 5² = 1.732 × 25 = 43.3 cm²
Calculate the surface area of an equilateral triangular pyramid where each side is 7 cm long.
Explanation
Surface Area = 84.87 cm²
Problem 4
Surface Area = √3 × a² = 1.732 × 7² = 1.732 × 49 = 84.868 cm²
The surface area of an equilateral triangular pyramid is 150 cm². Find the edge length of each triangle.
Explanation
Edge Length = 8.16 cm
It is the total area that covers the outer surface of the pyramid, including all its triangular faces.
1.How many faces does an equilateral triangular pyramid have?
2.What is the formula for the area of an equilateral triangle?
3.What is the difference between surface area and volume?
4.In what units is surface area measured?
Common Mistakes and How to Avoid Them in the Surface Area of an Equilateral Triangular Pyramid
Students often make mistakes while calculating the surface area of an equilateral triangular pyramid, which leads to incorrect results. Below are some common mistakes and the ways to avoid them.
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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
