102 LearnersLast updated on 30 August 2025
Surface Area of Equilateral Triangle
An equilateral triangle is a 2-dimensional shape with all three sides of equal length. The surface area of an equilateral triangle refers to the total area covered by its surface. In this article, we will learn about the surface area of an equilateral triangle.
What is the Surface Area of an Equilateral Triangle?
The surface area of an equilateral triangle is the total area occupied by its boundary.
It is measured in square units.
An equilateral triangle is a 2D shape with three equal sides and three equal angles, each measuring 60 degrees.
Equilateral triangles have a unique property where height and sides maintain a specific ratio.
Surface Area of an Equilateral Triangle Formula
An equilateral triangle's surface area can be calculated using a specific formula derived from its geometric properties.
The formula for the area of an equilateral triangle is:
Area = (√3/4) × side² square units
Where 'side' is the length of one side of the equilateral triangle.
This formula arises from the relation between the height and the side length of the triangle.
Derivation of the Surface Area Formula
To derive the formula for the surface area of an equilateral triangle, consider the properties of the triangle: every side is equal, and every angle is 60 degrees.
The height can be calculated using the Pythagorean theorem, which ends up being:
Height = (√3/2) × side
Substituting this into the standard triangle area formula (1/2 × base × height), we get:
Area = 1/2 × side × (√3/2) × side
Simplifying this expression yields: Area = (√3/4) × side²
Common Mistakes and How to Avoid Them in the Surface Area of an Equilateral Triangle
Students often make mistakes while calculating the surface area of an equilateral triangle, which leads to incorrect answers. Below are some common mistakes and the ways to avoid them.
Confusing the Formula
Students often confuse the formula for the area of an equilateral triangle with other triangle area formulas.
Remember, the formula specific to an equilateral triangle is Area = (√3/4) × side².
Using Incorrect Side Length
Students sometimes use incorrect side lengths, especially when given the perimeter instead of the side length. Always ensure you're using the length of one side.
Mistake 1
Misusing the Formula
The formula for an equilateral triangle’s area is specific and different from that of other triangles. Make sure to use Area = (√3/4) × side².
Mistake 2
Calculating Angles Incorrectly
Some students mistakenly calculate angles when unnecessary. Remember, all angles in an equilateral triangle are 60 degrees, so angle calculations are not needed for area.
Mistake 3
Using the Wrong Value for √3
A common mistake is using an incorrect approximation for √3. Use √3 ≈ 1.732 for precise calculations.
Mistake 4
Forgetting Units
Students often forget to include the correct units. Always express the area in square units, like cm² or m².
Mistake 5
Solved Examples of Surface Area of Equilateral Triangle
Find the area of an equilateral triangle with a side length of 8 cm.
Area = 27.71 cm²
Problem 1
Given side = 8 cm. Use the formula: Area = (√3/4) × side² = (1.732/4) × 8² = 0.433 × 64 = 27.71 cm²
Calculate the area of an equilateral triangle with a side length of 10 cm.
Explanation
Area = 43.30 cm²
Problem 2
Use the formula: Area = (√3/4) × side² = (1.732/4) × 10² = 0.433 × 100 = 43.30 cm²
An equilateral triangle has a perimeter of 30 cm. Find its area.
Explanation
Area = 43.30 cm²
Problem 3
Side length = Perimeter/3 = 30/3 = 10 cm Use the formula: Area = (√3/4) × side² = (1.732/4) × 10² = 43.30 cm²
Find the area of an equilateral triangle with a side length of 6 cm.
Explanation
Area = 15.59 cm²
Problem 4
Area = (√3/4) × side² = (1.732/4) × 6² = 0.433 × 36 = 15.59 cm²
If the area of an equilateral triangle is 64√3 cm², find the length of its side.
Explanation
Side length = 16 cm
It is the total area covered by the triangle's surface, calculated using the formula Area = (√3/4) × side².
1.What is the formula for the area of an equilateral triangle?
2.How are the angles in an equilateral triangle?
3.Can the perimeter be used to find the area?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of an Equilateral Triangle
Students often make mistakes while calculating the surface area of an equilateral triangle. Below are some common mistakes and the 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
