Perimeter of a Triangle Notes

Published on: September 29, 2026

This Perimeter of a Triangle Calculator finds the distance all the way around a triangle from the lengths of its three sides, and shows the working line by line. The three sides are independent, so each one is measured separately and every side is counted exactly once. Three lengths that cannot close into a triangle are rejected before any adding happens. Following the same pattern every time is what makes the perimeter of a triangle easy to picture, check, and work out on your own.

Triangle labeled a, b, c

In the diagram, the sides are labeled \(a\), \(b\) and \(c\).

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the three side lengths into the formula.
  4. Add the side lengths to get the perimeter.

Formula:

\(P = a + b + c\)
See Example 1 Hide Example 1

Problem

\(a = 6, b = 8, c = 10\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the three side lengths into the formula.
  4. Add the side lengths to get the perimeter.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the perimeter of a triangle whose side lengths are \(a = 6\), \(b = 8\) and \(c = 10\).

\(a = 6,\; b = 8,\; c = 10\)

Step 2

Step 2 - Write the formula.

In this problem: The perimeter is the distance all the way around the shape, and a triangle is made of three sides, so every side is counted once.

\(P = a + b + c\)

Step 3

Step 3 - Substitute the three side lengths into the formula.

In this problem: Replacing \(a\), \(b\) and \(c\) with \(6\), \(8\) and \(10\) in \(P = a + b + c\) gives \(P = 6 + 8 + 10\).

\(P = 6 + 8 + 10\)

Step 4

Step 4 - Add the side lengths to get the perimeter.

In this problem: Adding the three side lengths gives \(6 + 8 + 10 = 24\).

\(P = 6 + 8 + 10 = 24\)

Final Answer

\(P = 24\)
See Example 2 Hide Example 2

Problem

\(a = 5, b = 5, c = 6\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the three side lengths into the formula.
  4. Add the side lengths to get the perimeter.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the perimeter of a triangle whose side lengths are \(a = 5\), \(b = 5\) and \(c = 6\).

\(a = 5,\; b = 5,\; c = 6\)

Step 2

Step 2 - Write the formula.

In this problem: The perimeter is the distance all the way around the shape, and a triangle is made of three sides, so every side is counted once.

\(P = a + b + c\)

Step 3

Step 3 - Substitute the three side lengths into the formula.

In this problem: Replacing \(a\), \(b\) and \(c\) with \(5\), \(5\) and \(6\) in \(P = a + b + c\) gives \(P = 5 + 5 + 6\).

\(P = 5 + 5 + 6\)

Step 4

Step 4 - Add the side lengths to get the perimeter.

In this problem: Adding the three side lengths gives \(5 + 5 + 6 = 16\).

\(P = 5 + 5 + 6 = 16\)

Final Answer

\(P = 16\)
See Example 3 Hide Example 3

Problem

\(a = 7, b = 9, c = 12\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the three side lengths into the formula.
  4. Add the side lengths to get the perimeter.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the perimeter of a triangle whose side lengths are \(a = 7\), \(b = 9\) and \(c = 12\).

\(a = 7,\; b = 9,\; c = 12\)

Step 2

Step 2 - Write the formula.

In this problem: The perimeter is the distance all the way around the shape, and a triangle is made of three sides, so every side is counted once.

\(P = a + b + c\)

Step 3

Step 3 - Substitute the three side lengths into the formula.

In this problem: Replacing \(a\), \(b\) and \(c\) with \(7\), \(9\) and \(12\) in \(P = a + b + c\) gives \(P = 7 + 9 + 12\).

\(P = 7 + 9 + 12\)

Step 4

Step 4 - Add the side lengths to get the perimeter.

In this problem: Adding the three side lengths gives \(7 + 9 + 12 = 28\).

\(P = 7 + 9 + 12 = 28\)

Final Answer

\(P = 28\)
See Example 4 Hide Example 4

Problem

\(a = 4.5, b = 6, c = 7.5\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the three side lengths into the formula.
  4. Add the side lengths to get the perimeter.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the perimeter of a triangle whose side lengths are \(a = 4.5\), \(b = 6\) and \(c = 7.5\).

\(a = 4.5,\; b = 6,\; c = 7.5\)

Step 2

Step 2 - Write the formula.

In this problem: The perimeter is the distance all the way around the shape, and a triangle is made of three sides, so every side is counted once.

\(P = a + b + c\)

Step 3

Step 3 - Substitute the three side lengths into the formula.

In this problem: Replacing \(a\), \(b\) and \(c\) with \(4.5\), \(6\) and \(7.5\) in \(P = a + b + c\) gives \(P = 4.5 + 6 + 7.5\).

\(P = 4.5 + 6 + 7.5\)

Step 4

Step 4 - Add the side lengths to get the perimeter.

In this problem: Adding the three side lengths gives \(4.5 + 6 + 7.5 = 18\).

\(P = 4.5 + 6 + 7.5 = 18\)

Final Answer

\(P = 18\)