What is the Perimeter of Triangle?

Introduction

A triangle is an important shape that holds relevance not only in mathematics but also in our lives, from construction to transposition. Learning to calculate the perimeter of a triangle is a highly important skill that holds relevance in our lives. By understanding the properties of different types of triangles and their perimeter formulas explained on this page, students can quickly grasp the core concepts required for solving math problems based on this topic. 

Table of Contents

• What is Perimeter of Triangle?
• Properties of Triangle
• Types of Triangles
• Perimeter of Triangle Formula
• Application of Perimeter of Triangle
• Sample Problems on Perimeter of Triangle
• Frequently Asked Questions

What is the Perimeter of Triangle?

The perimeter of a triangle is defined as the total of the measures of its three sides. It is denoted by the letter ‘P’ and is equal to the sum of the lengths of all sides, i.e., Side-1 + Side-2 + Side-3 

The general formula for the perimeter of a triangle is P = a + b + c, where a, b and c are the lengths of the three sides. 

Properties of a Triangle

A triangle is a three-sided figure with three angles and three vertices. Key properties of a triangle are listed below:

1. Angle Sum Property: The sum of the angles of a triangle is always 180°

2. Exterior Angle Property: The measure of an exterior angle is equal to the sum of opposite interior angles.

3. Congruency of Triangles: Two triangles are similar or congruent if the sides and angles are identical.

Types of Triangles

Based on the properties of a triangle, it is classified into different types. If the length of all the sides of a triangle is equal, it is called an equilateral triangle (equal-side); if two sides of a triangle are equal, it is called an isosceles triangle, and if none of the sides are equal, it is known as a scalene triangle. 

• An equilateral triangle is a triangle with three equal sides and angles with a measure of 60° each. 

• An isosceles triangle is a triangle with two equal sides.

• A scalene triangle is a triangle with no equal sides.

Perimeter of Triangle Formula

Formula to find perimeter of different types of triangles – equilateral, isosceles and scalene

 

Application of Perimeter of Triangle 

The triangle is widely used in construction, designing, engineering and many other disciplines. Here are some of the ways in which the concept of the perimeter of triangles is applied:

1. Land Surveys:

Triangles are instrumental in determining the area and length of plots. By applying triangulation, surveyors can easily calculate distances and areas by dividing land into triangles and measuring their sides and angles.

2. Construction & Engineering:

A triangle is a highly reliable structure for building frameworks, roofs and bridges. The concept of the area of triangle is used in the estimation of cost and material, like roof sections or panels.

3. Physics and Mechanics:

Both triangles and trigonometry are used to analyse forces and motion, especially in situations involving inclined planes or angled objects. Understanding the basic concept of triangles and calculating its perimeter and area is foundational for trigonometry, which is applied in physics and engineering.

4. Everyday Applications:

Sandwiches, hangers, and even some musical instruments (like the triangle) are examples of triangular shapes in daily life.

Carpenters use right-angled triangles for measurements and to calculate distances in construction projects.

Sample Problems on Perimeter of Triangle

Example 1: Find the perimeter of an isosceles triangle if the length of equal sides is 4 cm and the third side is 5 cm.

Solution: Given that,

Side A = 4 cm Side B = 5 cm and Side C = 4 cm

We know that the formula for perimeter of an isosceles triangle is P = (2 x A) + B

Now, substitute the values in the formula

The perimeter of an isosceles triangle is (2 × A) + B

P = 2 × 4 + 5 =  13 cm

Example 2: Find the perimeter of a triangle with equal sides measuring to 5 cm.

Solution: Given: Length of the equal arms of an equilateral triangle = 5 cm

We know that the formula to calculate the perimeter of an equilateral triangle is  P = 3a 

Now, substitute the values in the perimeter formula; we get

P = 3(5) = 15 cm

Hence, the perimeter of an equilateral triangle is 15 cm. 

Conclusion

Learning how to calculate the perimeter of a triangle is an important skill that we need to master from early grades. Triangle is among one of the most basic structures used in engineering, architecture, design, construction, and so much more. It is one of the most reliable structures based on its strength and properties. Some of the most common examples of the application of perimeter of triangles formulas are rooftops and supportive structures in bridges.

Frequently Asked Questions on Perimeter of Triangle

1. What is the formula to find the perimeter of a triangle?

Answer: The general formula to find the perimeter of a triangle is P = a + b + c, where a, b and c are the lengths of the sides of a triangle, respectively. Depending on the type of triangle, the formula changes. The formula for an equilateral triangle is P = 3a and the formula for finding the perimeter of an isosceles triangle is P = 2a + b

P = a + b + c

2. What are the properties of a triangle?

Answer: Properties of a triangle are listed as under:

• There are three sides, three vertices & three angles in a triangle.

• The sum of angles of a triangle is always equal to 180°.

• The measure of an exterior angle is equal to the sum of opposite interior angles.

3. How to find the perimeter of an isosceles triangle?

Answer: The formula used to find the perimeter of an isosceles triangle is P = 2a + b, where a is the length of the equal sides and b is the length of the third side.

4. What is a scalene triangle?

Answer: A triangle is said to be a scalene triangle when none of its sides are equal to each other.