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Created By : Abhinandan Kumar

Reviewed By : Rajashekhar Valipishetty

Last Updated : Apr 21, 2023


Perimeter of Triangle -The perimeter of a triangle is the distance covered around the triangle and is calculated as the sum of all the three sides of it.

Perimeter of a Triangle Calculator

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What is the Perimeter of a Triangle?

The definition of the Perimeter of a Triangle is a distance around the shape ie., Triangle. In other words, the perimeter of any 2D closed figure or shape= sum of all its sides. The formula of the Perimeter of a Triangle is illustrated below with a detailed explanation.

Let's have a look at the formulas and memorize them carefully to find the Perimeter of a Triangle in just a fraction of seconds.

Perimeter of a Triangle formula

1. The most commonly used formula for finding the perimeter of a triangle is by adding all sides. i.e., Triangle Perimeter = a + b + c.

2. Yet, you won't give three sides always. In this scenario you can do like this, use the law of cosines to find the missing side:

c = √(a² + b² - 2ab * cos(γ))

This can be combined into the perimeter formula, i.e., Triangle Perimeter = a + b + √(a² + b² - 2ab * cos(γ)).

3. One more option is using the law of sines, in case you have one side and the two angles that are formed by that side:

b = sin(β) * a / sin(β + γ)

c = sin(γ) * a / sin(β + γ)

So the triangle perimeter may be stated as Triangle Perimeter = a + (a / sin(β + γ)) * (sin(β) + sin(γ)).

How to Find Perimeter of a Triangle?

Finding the perimeter of a triangle means finding the distance around the triangle. The simplest way to find the perimeter of a triangle is to add up the length of all of its sides, but if you don't know all of the side lengths you will need to calculate them first by using other suitable formulas.

1. Finding the Perimeter of a Triangle with all three sides (SSS):

The formula for the perimeter of a closed shape is normally equal to the length of all sides of the shape. Therefore, in the case of a triangle, the perimeter will be the sum of all the three sides.

For a triangle to exist some conditions need to be met and they are as follows,

a+b> c

b+c> a

c+a> b

Hence, the formula for the Perimeter of a Triangle when you have all sides is, P= a+b+c.

Where, a, b, c designates the sides of the triangle.

Solved Examples

Question 1: Find the Perimeter of a Triangle whose sides are 4 centimeters, 3 centimeters, and 2 centimeters?

Solution:

First, take the given triangle sides, they are 4 cm, 3 cm, and 2 cm.

Assume a = 4 cm, b = 3 cm and c = 2 cm then calculate triangle perimeter.

The formula for Perimeter of a triangle = Sum of all sides

⇒ P = a + b + c

⇒ Perimeter = 4 cm + 3 cm + 2 cm = 9.0 cm.

Here it met all three conditions, so Perimeter of a Triangle whose sides are 4 cm, 3 cm, and 2 cm is 9.0 cm.

Question 2: Find the perimeter of an equilateral triangle whose side is 2 cm?

Solution:

Being an equilateral triangle, all the sides are equal.

Thus, a = 2

Perimeter of an equilateral triangle= a + b + c = a + a + a = 3a

= 3 x a = 3 x 2

= 6 cm

Therefore, Perimeter of an equilateral triangle whose sides are equal i.e., a=2 cm is 6.0 cm.

Question 3: Find the perimeter of an isosceles triangle whose sides are equal sides is 4 cm and the third side is 6 cm?

Solution:

Being an isosceles triangle, two sides are equal.

Thus, a = 4, b = 4 and c = 6

Perimeter of an isosceles triangle= a +b + c = a + a + c = 2a + c

= 2 x a + 8 = 2 x 4 + 6

= 14 cm

Therefore, Perimeter of an isosceles triangle whose sides are 4 cm, 4cm, and 6 cm is 14.0 cm.

2. Finding the Perimeter of a Triangle with Two Sides and Angle between them (SAS):

  • First and foremost, take the given length of two sides and angle of one side.
  • Use the law of cosines to calculate the third side and then find the perimeter of a triangle.
  • The formula to find the third side is c= √(a² + b² - 2ab * cos(γ)).‚Äč
  • Now place the length and angle values in the above formula and calculate the C length.
  • After finding the C value, easily you can find the perimeter of a triangle(SAS) using formula i.e., P = a+b+c.

3. Finding the Perimeter of a Triangle with one side and two angles (ASA):

For suppose, you have input say two angles and one length of the triangle then this method will be helpful for you to calculate the perimeter of a triangle easily:

  • Initially, write down all given inputs here and then use the law of sines to find the other two sides of the triangle.
  • The formulas you need to apply to calculate two sides are b = sin(β) * a / sin(β + γ) and c = sin(γ) * a / sin(β + γ).
  • Apply the input angles and one length value in the above formulas and calculate the two side values.
  • Finally, we have all three sides lengths so apply them in the formula of the perimeter of a triangle(ASA) i.e., P= a+b+c.

How to Use our Perimeter of a Triangle calculator?

By following the below simple steps you will completely understand how to use our Perimeter of a Triangle Calculator. Once you know how it works then you will surely love our online free calculator to find triangle perimeter.

  1. Firstly, you should give your inputs in the respective fields available on the screen.
  2. Then, select the units like cm,m, ft, yd, mi, etc. by clicking on the desired one from the drop-down list.
  3. After giving all your required inputs, simply tap on the blue colored "Perimeter" button.
  4. Later, our Perimeter of a Triangle Calculator displays the solution below the button along with a detailed explanation.

FAQs on Finding Triangle Perimeter

1. How do you find the perimeter of a triangle?

Memorize the Perimeter of a triangle formula and easily find the result for your inputs. For example, If you take a triangle with sides a, b and c, the perimeter P is defined as P = a + b + c.

2. What is the sum of the perimeter of a triangle?

The Perimeter of the Triangle = Sum of the Sides. For instance, if you enter a=2 cm, b=4 cm, c=3 cm then the triangle perimeter = 2 cm + 4 cm + 3 cm (add the length of each side of the triangle).

3. Can a triangle have the same area and perimeter?

The area is measured in square units and the perimeter is measured in length units. Any triangles with the same perimeter and area and with one side the same are congruent.

4. What is meant by the Perimeter of a Triangle?

The perimeter of a triangle is the total distance around the edges of a triangle. In a nutshell, the length of the boundary of a triangle is its perimeter.