101 LearnersLast updated on July 31st, 2025
Surface Area of Tetrahedron
A tetrahedron is a 3-dimensional shape that consists of four triangular faces. The surface area of a tetrahedron is the total area covered by its outer surface, which is the sum of the areas of its four triangular faces. In this article, we will learn about the surface area of a tetrahedron.
What is the Surface Area of a Tetrahedron?
The surface area of a tetrahedron is the total area occupied by the boundary or surface of a tetrahedron. It is measured in square units.
A tetrahedron is a 3D shape with four triangular faces, six edges, and four vertices. It is one of the simplest types of polyhedra.
The most common type of tetrahedron is the regular tetrahedron, where all four faces are equilateral triangles, and all edges are of equal length.
Surface Area of a Tetrahedron Formula
A tetrahedron consists of four triangular faces. To find its surface area, you calculate the area of each triangular face and sum them up.
For a regular tetrahedron with side length 'a', the formula for the surface area is: Surface Area = √3 * a² square units
Surface Area of a Regular Tetrahedron
For a regular tetrahedron, where all faces are equilateral triangles, the surface area can be calculated using the formula:
Surface Area = √3 * a²
Here, 'a' is the length of a side of the tetrahedron.
Each face being an equilateral triangle simplifies the computation, as all faces are identical.
Surface Area of an Irregular Tetrahedron
For an irregular tetrahedron, where the triangular faces are not necessarily equilateral, the surface area is the sum of the areas of its four triangular faces. You can use Heron's formula to find the area of each triangular face if the lengths of the sides are known.
Volume of a Tetrahedron
The volume of a tetrahedron shows how much space is inside it. For a regular tetrahedron with side length 'a', the volume can be found by using the formula: Volume = (a³√2) / 12 (cubic unit)
Confusion between Regular and Irregular Tetrahedrons
Students often confuse regular and irregular tetrahedrons. Remember, a regular tetrahedron has all equal sides and equilateral triangular faces, whereas an irregular one does not.
Mistake 1
Using Incorrect Formula for Irregular Tetrahedrons
Some students mistakenly apply the formula for a regular tetrahedron to an irregular one. For irregular tetrahedrons, calculate the area of each triangular face separately and sum them.
Mistake 2
Forgetting to Square Side Length in Formula
A common mistake is forgetting to square the side length when using the formula for the surface area of a regular tetrahedron. Make sure to square the side length 'a' in the formula.
Mistake 3
Assuming All Tetrahedrons are Regular
Students sometimes assume that all tetrahedrons are regular. This assumption can lead to incorrect calculations. Always confirm the type of tetrahedron before applying formulas.
Mistake 4
Using Wrong Units
Ensure that all measurements are in the same unit before calculating the surface area. Surface area should always be expressed in square units.
Mistake 5
Solved Examples of Surface Area of Tetrahedron
Find the surface area of a regular tetrahedron with side length 6 cm.
Surface Area = 62.35 cm²
Problem 1
Given a = 6 cm. Use the formula: Surface Area = √3 * a² = √3 * 6² = √3 * 36 ≈ 62.35 cm²
A regular tetrahedron has a side length of 10 cm. Find its surface area.
Explanation
Surface Area = 173.21 cm²
Problem 2
Use the formula: Surface Area = √3 * a² = √3 * 10² = √3 * 100 ≈ 173.21 cm²
Find the surface area of a regular tetrahedron with side length 8 cm.
Explanation
Surface Area = 110.85 cm²
Problem 3
Use the formula: Surface Area = √3 * a² = √3 * 8² = √3 * 64 ≈ 110.85 cm²
Calculate the surface area of a regular tetrahedron with side length 5 cm.
Explanation
Surface Area = 43.30 cm²
Problem 4
Surface Area = √3 * a² = √3 * 5² = √3 * 25 ≈ 43.30 cm²
A regular tetrahedron has a side length of 12 cm. Find its surface area.
Explanation
Surface Area = 249.44 cm²
It is the total area that covers the outside of the tetrahedron, which is the sum of the areas of its four triangular faces.
1.What is the formula for the surface area of a regular tetrahedron?
2.Can the formula for a regular tetrahedron be applied to an irregular one?
3.Is a regular tetrahedron the same as an equilateral tetrahedron?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Tetrahedron
Students often make mistakes while calculating the surface area of a tetrahedron, which leads to wrong 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
: She has songs for each table which helps her to remember the tables
