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149 LearnersLast updated on September 26, 2025
Perimeter of Equilateral Triangle
The perimeter of a shape is the total length of its boundary. In the case of an equilateral triangle, the perimeter is the sum of all three equal sides. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of an equilateral triangle.
What is the Perimeter of an Equilateral Triangle?
The perimeter of an equilateral triangle is the total length of its three equal sides. By adding the length of all three sides, we get the perimeter of the shape.
The formula for the perimeter of an equilateral triangle is \( P = 3a \), where \( a \) is the length of a side of the triangle. For instance, if an equilateral triangle has sides \( a = 6 \), then its perimeter is \( P = 3 \times 6 = 18 \).
Formula for the Perimeter of Equilateral Triangle - \( P = 3a \).
Let’s consider another example of an equilateral triangle with side length \( a = 10 \).
So the perimeter of the equilateral triangle will be: \( P = 3a = 3 \times 10 = 30 \).
How to Calculate the Perimeter of an Equilateral Triangle
To find the perimeter of an equilateral triangle, simply apply the formula ( P = 3a ), where ( a ) is the length of one side of the triangle. For instance, if a given equilateral triangle has sides of ( a = 8 ), then the perimeter is ( P = 3 times 8 = 24 ) cm.
Example Problem on Perimeter of Equilateral Triangle
For finding the perimeter of an equilateral triangle, we use the formula ( P = 3a ).
For example, let’s say ( a = 7 ) cm. Now, the perimeter = ( 3 \times 7 = 21 ) cm.
Therefore, the perimeter of the equilateral triangle is 21 cm.
Tips and Tricks for Perimeter of Equilateral Triangle
Learning some tips and tricks makes it easier for children to calculate the perimeter of equilateral triangles. Here are some tips and tricks given below: Always remember that an equilateral triangle's perimeter is simply three times the length of one side.
For that, use the formula ( P = 3a ). In problems, if the side length of an equilateral triangle is not directly given, you may need to calculate it using other provided information like coordinates, using the distance formula: Distance = (sqrt{(x_2-x_1)2+(y_2-y_1)2}). Here, ((x_1, y_1)) and ((x_2, y_2)) indicate the positions of two points.
To avoid mistakes when adding the perimeter, make sure the side lengths are precise and constant for common uses like gardening and architecture. If you are given the semi-perimeter, which is half the perimeter, you can multiply it by 2 to determine the full perimeter. Area-related calculations, like using altitude or height, often use the semi-perimeter.
Common Mistakes and How to Avoid Them in Perimeter of Equilateral Triangle
Did you know that while working with the perimeter of an equilateral triangle, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Using the formula for a non-equilateral triangle when dealing with equilateral triangles.
Remember that for equilateral triangles, the correct formula is ( P = 3a ).
Using other formulas meant for different types of triangles will lead to incorrect results.
Mistake 2
Confusing side length with perimeter, leading to incorrect calculations.
It is important to note that the perimeter is calculated by multiplying the side length by 3 for equilateral triangles, while the side length is just one side of the triangle.
Mistake 3
Assuming a triangle is equilateral without verifying side lengths, resulting in inaccurate calculations.
Always verify that the triangle is equilateral by checking that all sides are equal before using the perimeter formula for equilateral triangles.
Mistake 4
Using incorrect units for the perimeter, which may cause confusion.
Double-check the units provided and ensure that you use the correct units for your calculations.
Mistake 5
Misunderstanding or misidentifying the value of the side length in a problem outline.
Before starting the calculations, make sure that you understand the problem and, if it's possible, try to draw a triangle to accurately identify the side lengths.
Perimeter of Equilateral Triangle Examples
Problem 1
A garden has an equilateral triangular shape with a perimeter of 60 meters. If two sides are 20 meters each, what is the length of the third side?
20 meters
Explanation
Let ( a ) be the side of the equilateral triangle.
Since it is equilateral, all sides are equal.
The given perimeter = 60 meters.
Perimeter of equilateral triangle = ( 3a ) ( 60 = 3a ) ( a = frac{60}{3} = 20 )
Therefore, each side, including the third side, is 20 meters.
Problem 2
A wire with a perimeter of 297 inches is reshaped into an equilateral triangle. Find the length of each side of the triangle.
99 inches
Explanation
Given that the total length of the wire is used to form an equilateral triangle, the solution is:
Perimeter of the equilateral triangle = ( 3a ) ( 297 = 3a ) ( a = frac{297}{3} = 99 )
Therefore, the length of each side of the triangle is 99 inches.
Problem 3
Find the perimeter of an equilateral triangle whose sides are 9 cm.
27 cm
Explanation
Perimeter of equilateral triangle = ( 3a ) ( P = 3 times 9 = 27 )
Therefore, the perimeter of the triangle is 27 cm.
Problem 4
A playground has an equilateral triangular layout with each side measuring 15 meters. How much fencing is needed to go around the playground?
45 meters of fencing is needed.
Explanation
The perimeter of an equilateral triangle is the sum of all three equal sides.
Using the formula: ( P = 3a ) ( P = 3 times 15 = 45 ) meters.
Problem 5
Find the perimeter of an equilateral triangular tile with each side measuring 7 inches.
21 inches
Explanation
The perimeter of an equilateral triangle is calculated by summing the lengths of its three equal sides: ( P = 3a = 3 \times 7 = 21 ) inches.
FAQs on Perimeter of Equilateral Triangle
1.Evaluate the perimeter of an equilateral triangle if its sides are 5 cm.
2.What is meant by an equilateral triangle’s perimeter?
3.What are the properties of an equilateral triangle?
4.How do you find the perimeter of an equilateral triangle?
5.Can an equilateral triangle be a right triangle?
Important Glossaries for Perimeter of Equilateral Triangle
- Perimeter: The total length of the boundary of a shape.
- Equilateral Triangle: A triangle with all three sides of equal length and all angles equal to 60 degrees.
- Formula for Perimeter: The mathematical expression used to calculate the perimeter of an equilateral triangle is ( P = 3a ).
- Side Length: The measure of one side of a triangle, particularly used in equilateral triangles where all sides are equal.
- Symmetry: A property where a shape looks the same when viewed from different angles, common in equilateral triangles.
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
