How To Find The Perimeter Of A Triangle?

how to find the perimeter of a triangle

We all studied how to find the perimeter of a triangle during our maths lecture in school. Generally, a triangle is a polygon that has three sides. It is classified into different types based on the measurement of its sides and angles. In my today’s post, I will teach you how to find the perimeter and area of a triangle in detail. There are different formulas for calculating the perimeter and area of a triangle based on its type. Without wasting much time, let us check out how to find the perimeter of a triangle a bit more in detail.

How To Find The Perimeter Of A Triangle?

Using the following three ways, you can easily learn how to find the perimeter of a triangle.

  • Method 1: When All The Three Sides Are Known
  • Method 2: By Using The Pythagorean Theorem
  • Method 3: By Using The Law Of Cosines

There are three types of triangles: equilateral triangle, isosceles triangle, and scalene triangle. Do you know the definition of perimeter? It means the sum of all three sides. Therefore, the perimeter of a triangle will be the sum of its three sides.

You can keep on reading to learn how to find the perimeter of a triangle in detail.

Find The Perimeter Of A Triangle When Three Sides Are Known

The formula for finding the perimeter of a triangle with sides a, b, and c is P = a + b + c. So, you can follow these steps for how to find the perimeter of an equilateral triangle.

  1. First, check the length of all three sides of the triangle.
  2. Then, add the three side lengths together to find the perimeter.
  3. You can add the units (centimeters) in your final answer.

This formula for the perimeter of a triangle is the same for any kind of triangle. You can now keep on reading to check out how to find the perimeter of a triangle with one side missing.

Find The Perimeter Of A Triangle Using Pythagorean Theorem

A right-angled triangle is a triangle that usually has one right angle. One side of the triangle is always the longest side (opposite to the right angle). It’s called the hypotenuse.

Using the following instructions you can learn how to find the perimeter of a right triangle.

  1. First, recall and note down the Pythagorean Theorem: a2 + b2 = c.
  2. Next, label all sides of the triangle as “a”, “b”, and “c”.
  3. Now, substitute the side lengths into the Pythagorean Theorem.
  4. You have to solve this equation if the length of any side of the triangle is missing.
  5. Lastly, add up the lengths of all three sides of the triangle to find its perimeter.

While using this method, you must know the square roots of the side lengths. This means you have to multiply each value by itself (for example 32 = 3 * 3 = 9).

Find The Perimeter Of A Triangle Using The Law Of Cosines

The Law of Cosines allows you to calculate the side and perimeter of any triangle. Follow these steps to find out how to find the perimeter of the triangle with the Law of Cosine.

  1. First, recall and note down the Law of Cosine: c2 = a2 + b2 – 2ab cos(C).
  2. Next, label all sides of the triangle as “a”, “b”, and “c”.
  3. Now, substitute the side lengths into the Law of Cosine.
  4. Find the cosine of C by using the cos function on your calculator.
  5. Then, solve the equation to get the value of c.
  6. Lastly, add up the lengths of all three sides of the triangle to find its perimeter.

Here, the angle between two sides of a triangle will be used to find the cosine of C. If the value of the cosine of C is negative, you have to carry the minus symbol in the equation. 

You can continue to read to learn how to find the perimeter of a triangle with variables.

Find The Perimeter Of A Triangle On The Graph

Many people find difficulty in calculating the perimeter of a triangle in a coordinate plane. Sometimes, there are no horizontal and vertical sides. In that case, you can follow these steps to learn how to find the perimeter of a triangle on a graph.

  1. For this method, you’ll need the coordinates of A(x1,y1),B(x2,y2),C(x3,y3).
  2. Now, find the lengths of the three sides using the distance formula d=√(x2−x1)2+(y2−y1)2.
  3. This will give you the values for (AB)2, (BC)2, and (AC)2.
  4. Add the three distance values into the perimeter formula.

Remember that the lengths of the sides are the distances between two points.

Find The Perimeter Of A Triangle Along A Circle Inside

Do you know how to calculate the perimeter of a triangle with a circle inside? Using the same perimeter formula (P=a+b+c), you can calculate the triangle’s perimeter. For this, you need to know all three sides of the triangle.

Find The Area Of A Triangle

You can easily learn how to find the area of a triangle using the area of triangle formula. It is A= ½ ( b x h) square units. This formula is applicable to all types of triangles.

You can keep on reading to know how to find the perimeter of a rectangle and square.

Find The Perimeter Of A Rectangle And Square

A rectangle consists of two lengths and two breadths. So, the perimeter of a rectangle is defined as the sum of all sides of the rectangle. Use the P = 2 x (a + b) formula to get the perimeter of a rectangle.

A  square consists of four equal sides. Therefore, the perimeter of a square is defined as the distance covered by its four sides. Use the P = 4 x side formula to get the perimeter of a square.

Read more about different topics on Fyndblog

FAQ

How Do We Find The Perimeter Of A Triangle?

To calculate the perimeter of a triangle, add the length of its sides. For example, if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c.

What Is The Perimeter Of ∆ ABC?

To find the perimeter of \triangle ABC we use the Pythagorean Theorem which tells us that |AB|^2 = |AC|^2 + |BC|^2.

What Is The Formula For Perimeter?

The perimeter formula for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width. When you are given the dimensions of a rectangular shape, you can simply plug in the values of L and W into the formula in order to solve for the perimeter.

How Do You Find The 3rd Side Of A Triangle?

Different Ways to Find the Third Side of a Triangle
For a right triangle, use the Pythagorean Theorem. For an isosceles triangle, use the area formula for an isosceles. If you know some of the angles and other side lengths, use the law of cosines or the law of sines.

Conclusion

In the above post, I have discussed how to find the area and perimeter of a triangle with coordinates in detail. You can calculate the perimeter of a triangle by using the perimeter formula P = a + b + c. Otherwise, you can opt for the Pythagorean Theorem and the Law of Cosines to find the perimeter. Similarly, using the Law of Sines you can learn how to calculate the perimeter of a triangle with two sides missing. Use a calculator to get quick answers! You can now find the perimeter of any triangle by learning how to find the perimeter of a triangle.

 

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