Summarize this article:
102 LearnersLast updated on October 28, 2025
Base Area of an Equilateral Triangle
The base area of an equilateral triangle refers to the area of the flat surface, which is a 2-dimensional shape with equal sides. An equilateral triangle is a polygon with three equal sides and three equal angles, each measuring 60 degrees.
What is the Base Area of an Equilateral Triangle?
The base area of an equilateral triangle is the space enclosed by its three sides. It is a 2-dimensional shape with all sides and angles equal.
The area of an equilateral triangle can be calculated using a specific formula that incorporates its side length.
What is the Base Area of an Equilateral Triangle Formula?
The formula for the area of an equilateral triangle is: Area = (√3 / 4) * a2
In this formula, a = length of a side of the triangle.
How to Find the Base Area of an Equilateral Triangle?
The base area of an equilateral triangle can be found using the formula: Area = (√3 / 4) * a2
To use this formula, follow these steps:
Step 1: Determine the length of a side of the triangle and denote it as a.
Step 2: Substitute the side length into the formula to find the area.
Step 3: Write the answer with square units.
For example, if the side of an equilateral triangle is 6 cm, find the base area.
Base area = (√3 / 4) * 62 = (√3 / 4) * 36 = 9 * sqrt(3) ≈ 15.59 cm²
Tips and Tricks for the Base Area of an Equilateral Triangle
Here are some tips and tricks to help solve the problem easily.
- Remember all sides and angles are equal.
- Use the formula correctly.
- Check units.
- Ensure the side length is used, not the height.
- Avoid confusing with other triangle area formulas.
Common Mistakes and How to Avoid Them on the Base Area of an Equilateral Triangle
When finding the base area of an equilateral triangle, students make small mistakes, which lead to the wrong answers. Here are some common mistakes that can be avoided.
Mistake 1
Confusing side length with height
Students often mistakenly use the height instead of the side length in the formula. Always check that you are using the side length when applying the formula.
Mistake 2
Using the wrong formula
Some students mix up the equilateral triangle formula with that of other triangle types. The base area of an equilateral triangle is calculated using Area = (sqrt(3) / 4) * a^2.
Mistake 3
Forgetting to square the side length
First, square the side length (a^2), then multiply by (sqrt(3) / 4) to find the base area.
Mistake 4
Using incorrect value for square root of 3
Sometimes students use an incorrect value for sqrt(3). Use sqrt(3) ≈ 1.732 when a decimal approximation is needed.
Mistake 5
Calculating using height instead of side length
Students mistakenly use the height of the triangle directly in the formula. Always ensure the formula incorporates the side length, not the height.
Solved Examples for Base Area of an Equilateral Triangle
Problem 1
The side length of an equilateral triangle is 4 cm. Find the base area.
6.93 cm²
Explanation
To find the base area of the equilateral triangle, use the formula: Area = (√3 / 4) * a2
Side length a = 4 cm
Area = (√3 / 4) * 42 = (√3 / 4)* 16 = 4 * sqrt(3) ≈ 6.93 cm²
Problem 2
The side length of an equilateral triangle is 5.5 cm. Find the base area.
13.1 cm²
Explanation
To find the base area of the equilateral triangle: Area = (√3 / 4) * a2
Side length a = 5.5 cm
Area = (√3 / 4) * 5.52 = (√3 / 4) * 30.25 = 7.5625 * sqrt(3) ≈ 13.1 cm²
Problem 3
An equilateral triangle has a perimeter of 18 cm. Find the base area of the triangle.
15.59 cm²
Explanation
The perimeter of the triangle is 18 cm, so each side a = 18 / 3 = 6 cm.
Area = (√3 / 4) * 6^2 = (√3 / 4) * 36 = 9 * sqrt(3) ≈ 15.59 cm²
Problem 4
The base area of an equilateral triangle is 10.83 cm². Find the side length.
a = 5 cm
Explanation
To find the side length, use the area formula: Area = (√3 / 4)* a2
10.83 = (√3 / 4)* a2
a2 = 10.83 / (√3 / 4)a2 = 12.5
Take the square root of both sides: a = sqrt(12.5) a ≈ 5 cm
Problem 5
A triangular garden is shaped as an equilateral triangle with side length 9 m. Find its base area to determine the space available for planting.
35.07 m²
Explanation
The formula for the base area of an equilateral triangle is: Area = (√3 / 4) * a2
Side length a = 9 m
Area = (√3 / 4) * 92 = (√3 / 4) * 81 = 20.25 * sqrt(3) ≈ 35.07 m²
FAQs on Base Area of an Equilateral Triangle
1.What is the base area of an equilateral triangle?
2.What is the formula for the base area of an equilateral triangle?
3.How do you find the base area of an equilateral triangle with a given perimeter?
4.Is the base area the same as the area of the equilateral triangle?
5.What unit is used for the base area of an equilateral triangle?
Important Glossary for Base Area of an Equilateral Triangle
- Base Area: The area enclosed by the sides of an equilateral triangle, calculated using the formula (√3 / 4) * a2.
- Equilateral Triangle: A triangle with all three sides and angles equal.
- Side Length: The length of one side of the equilateral triangle.
- Perimeter: The total length around the triangle, equal to three times the side length.
- Square Root: A mathematical value that, when multiplied by itself, gives the original number; used in calculating the area of an equilateral triangle.
Explore More measurement
![Important Math Links Icon]()
Previous to Base Area of an Equilateral Triangle
![Important Math Links Icon]()
Next to Base Area of an Equilateral Triangle
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
