Summarize this article:
125 LearnersLast updated on December 11, 2025
Perimeter of Acute Triangle
The perimeter of a shape is the total length of its boundary. The sum of all three sides is called the perimeter of a triangle. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of an acute triangle.
What is the Perimeter of an Acute Triangle?
The perimeter of an acute triangle is the total length of its three sides.
By adding the length of all three sides, we get the perimeter of the shape.
The formula for the perimeter of an acute triangle is ๐ = ๐ + ๐ + ๐, where a, b, and c are the sides of the triangle.
For instance, if an acute triangle has sides, a = 5, b = 7, and c = 9, then its perimeter is p = 5 + 7 + 9 = 21.
Formula for Perimeter of Acute Triangle - ๐ท = ๐ + ๐ + ๐.
Let’s consider another example of an acute triangle with side lengths, ๐ = 7, ๐ = 11, and ๐ = 13.
So the perimeter of the triangle will be: ๐ท = ๐ + ๐ + ๐ = 7 + 11 + 13 = 31.
How to Calculate the Perimeter of an Acute Triangle
To find the perimeter of an acute triangle, we just need to apply the given formula and sum all the sides of the triangle.
For instance, a given acute triangle has the sides of a = 6, b = 8, c = 10.
Perimeter = sum of all sides = 6 + 8 + 10 = 24 cm.
Example Problem on Perimeter of Acute Triangle - For finding the perimeter of an acute triangle, we use the formula, ๐ท = ๐ + ๐ + ๐.
For example, let’s say, a = 3 cm, b = 4 cm, and c = 5 cm. Now, the perimeter = sum of all sides = 3 + 4 + 5 = 12 cm. Therefore, the perimeter of the acute triangle is 12 cm.
Explore Our Programs
Tips and Tricks for Perimeter of Acute Triangle
Learning some tips and tricks makes it easier for children to calculate the perimeter of acute triangles.
Here are some tips and tricks given below:
Always remember that an acute triangle's perimeter is simply the sum of the three sides of the shape. For that, use the formula, ๐ท = ๐ + ๐ + ๐.
Calculating the perimeter of an acute triangle starts by determining the length of each side using the distance formula.
The distance formula is: Distance = √((x2-x1)²+(y2-y1)²). Here, (x1, y1) and (x2, y2) indicate the positions of two points that make out a triangle’s side.
They can be found by adding the lengths of three sides after they are calculated.
To reduce confusion, specifically arrange the indicated side lengths if you need the perimeter of a group of triangles.
After that, apply the formula to each triangle.
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 Heron’s formula, often use the semi-perimeter.
Common Mistakes and How to Avoid Them in Perimeter of Acute Triangle
Did you know that while working with the perimeter of an acute triangle, children might encounter some errors or difficulties? We have many solutions to resolve these problems.
Here are some given below:
Mistake 1
Incorrectly using the Pythagorean theorem (a² + b² = c²) for triangles that are not right-angled.
Remember that only right-angled triangles can use the Pythagorean theorem.
The lengths of all the sides of other triangle types should be summed up to find the perimeter.
Mistake 2
Students may confuse the concepts of area and perimeter, leading to incorrect calculations.
It is important to note that the perimeter, calculated in linear units, is the total length of the triangle’s sides, while the area, in square units, represents the space inside the triangle.
Mistake 3
Assuming that every triangle is isosceles or equilateral, which results in inaccurate calculations.
A scalene triangle has all the sides of different lengths.
Always be careful about the type of the triangle’s type to ensure accurate calculations.
Mistake 4
Using the wrong values for the length of the sides, misreading a problem, or mislabeling the sides.
Double-check the problem and ensure that you're using the correct lengths for your triangle.
Mistake 5
Misunderstanding or misidentifying the side lengths that are given 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 Acute Triangle Examples
Problem 1
A triangular park has a perimeter of 50 meters and two sides measuring 18 meters each. To find out the missing side of the park, subtract the sum of the known sides from the total perimeter.
Length of the missing side = 14 meters.
Explanation
Let ‘b’ be the side of the missing side. And the given perimeter = 50 meters.
Length of the two equal sides = 18 meters.
Perimeter of triangle = sum of lengths of three sides.
50 = 18 + 18 + b 50 = 36 + b b = 50 – 36 = 14 b = 14
Therefore, the missing side is 14 meters.
Problem 2
A piece of string with a perimeter of 150 cm is reshaped into an equilateral triangle. Find the length of each side of the triangle and divide the total length by 3.
50 cm
Explanation
Given that the perimeter of a piece of string is equal to the total length of the wire and this wire is reshaped into an equilateral triangle, here is the solution:
Perimeter of a piece of string = Total length of the wire Length of the wire used = Perimeter of the triangle formed Perimeter of an equilateral triangle = 3 × a 150 = 3 × a 150 ÷ 3 = 50 a = 50
Therefore, the length of each side of the triangle is 50 cm.
Problem 3
Find the perimeter of an acute triangle whose sides are 8cm, 6cm, and 7cm.
21 cm
Explanation
Perimeter of triangle = a + b + c P = 8 + 6 + 7 = 21. Therefore, the perimeter of the triangle is 21 cm.
Problem 4
Emma is planning a triangular flower bed in her backyard. She measures the three sides of the flower bed: Side A = 10 meters Side B = 12 meters Side C = 14 meters How much fencing should Emma buy to go around the edge of the flower bed?
Emma will need 36 meters of fencing to go around the flower bed.
Explanation
The perimeter of a triangle is the sum of all the three sides.
Using the formula: P = a + b + c P = 10 + 12 + 14 = 36 meters.
Problem 5
Find the perimeter of the scalene triangular hill.
Sides are a = 11, b = 9, c = 8 Perimeter = a + b + c = 11 + 9 + 8 = 28 meters.
Explanation
Each side of the scalene triangle has a different length.
The entire distance is calculated around the hill to be 28 meters by summing the lengths of the three sides.
FAQs on Perimeter of Acute Triangle
1.Evaluate the triangleโs perimeter if its sides are 4cm, 6cm, and 8cm.
2.What is meant by a triangleโs perimeter?
3.What are the types of triangles?
4.Which triangle has no equal sides?
5.Which triangle has the smallest perimeter?
Important Glossaries for Perimeter of Acute Triangle
- Perimeter: The total length of the sides of a shape.
- Acute Triangle: A triangle where all the interior angles are less than 90 degrees.
- Scalene Triangle: A triangle with all three sides of different lengths.
- Equilateral Triangle: A triangle with all three sides equal in length.
- Formula of perimeter: The mathematical expression used to calculate the perimeter of a triangle is ๐ท = ๐ + ๐ + ๐.
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
