Perimeter of Acute Triangle
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Last updated on December 11, 2025

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 𝑃 = 𝑎 + 𝑏 + 𝑐, 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 - 𝑷 = 𝑎 + 𝑏 + 𝑐.

Let’s consider another example of an acute triangle with side lengths, 𝑎 = 7, 𝑏 = 11, and 𝑐 = 13.

So the perimeter of the triangle will be: 𝑷 = 𝑎 + 𝑏 + 𝑐 = 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, 𝑷 = 𝑎 + 𝑏 + 𝑐.

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.

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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, 𝑷 = 𝑎 + 𝑏 + 𝑐.

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:

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.

Okay, lets begin

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.

Well explained 👍

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.

Okay, lets begin

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.

Well explained 👍

Problem 3

Find the perimeter of an acute triangle whose sides are 8cm, 6cm, and 7cm.

Okay, lets begin

21 cm

Explanation

Perimeter of triangle = a + b + c P = 8 + 6 + 7 = 21. Therefore, the perimeter of the triangle is 21 cm.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of the scalene triangular hill.

Okay, lets begin

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.

Well explained 👍

FAQs on Perimeter of Acute Triangle

1.Evaluate the triangle’s perimeter if its sides are 4cm, 6cm, and 8cm.

Perimeter of triangle = a + b + c, Hence p = 4 + 6 + 8 = 18 cm.

2.What is meant by a triangle’s perimeter?

The total length around a triangle’s sides is its perimeter.

In other words, the perimeter of a triangle is the total length of its sides.

3.What are the types of triangles?

There are six types of triangles: Equilateral triangle, Isosceles triangle, Scalene triangle, Acute triangle, Right triangle, and Obtuse triangle.

4.Which triangle has no equal sides?

A scalene triangle is a triangle with no equal sides. All three sides of the scalene triangle are different.

5.Which triangle has the smallest perimeter?

The orthic 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 𝑷 = 𝑎 + 𝑏 + 𝑐.

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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