How to Find Perimeter of a Triangle with Vertices

The perimeter of a triangle is the sum of the lengths of its sides. To find the perimeter of a triangle given the coordinates of its vertices, you can use the distance formula to calculate the length of each side and then sum these lengths.

Steps to Find the Perimeter

1. Identify the coordinates of the vertices. Let the vertices be A(x_{A}, y_{A}), B(x_{B}, y_{B}), and C(x_{C}, y_{C}).
2. Calculate the length of each side using the distance formula:
   • For side AB: d_{AB} = \sqrt{(x_{B} - x_{A})^2 + (y_{B} - y_{A})^2}
   • For side BC: d_{BC} = \sqrt{(x_{C} - x_{B})^2 + (y_{C} - y_{B})^2}
   • For side CA: d_{CA} = \sqrt{(x_{A} - x_{C})^2 + (y_{A} - y_{C})^2}
3. Sum the lengths of the sides to get the perimeter: P = d_{AB} + d_{BC} + d_{CA}

Example Calculation

Let's find the perimeter of a triangle with vertices A(1, 2), B(4, 6), and C(5, 3).

Therefore, the perimeter of the triangle is 5 + \sqrt{10} + \sqrt{17} units.

Additional Resources

• For an online calculator to find the perimeter and area of a triangle given its vertices, visit .
• To explore more about the distance formula and its applications in finding the perimeter, see .
• For interactive learning and practice problems, check out .

Finding the perimeter of a triangle given its vertices involves calculating the distances between each pair of vertices and summing these distances. This method utilizes the distance formula in coordinate geometry, making it a straightforward yet powerful tool for solving geometry problems. In this article, we will guide you step-by-step on how to calculate the perimeter of a triangle using the coordinates of its vertices.

Let's consider a triangle with vertices A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃). The steps to find the perimeter are:

• Calculate the distance between vertex A and vertex B using the distance formula: \[ d_{AB} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
• Calculate the distance between vertex B and vertex C using the distance formula: \[ d_{BC} = \sqrt{(x_3 - x_2)^2 + (y_3 - y_2)^2} \]
• Calculate the distance between vertex C and vertex A using the distance formula: \[ d_{CA} = \sqrt{(x_3 - x_1)^2 + (y_3 - y_1)^2} \]
• Add the distances calculated to get the perimeter of the triangle: \[ \text{Perimeter} = d_{AB} + d_{BC} + d_{CA} \]

This method is applicable to any triangle in a coordinate plane, whether it is scalene, isosceles, or equilateral. It is particularly useful in various real-life applications such as land surveying, architecture, and computer graphics.

• Definition of a Triangle's Perimeter

• Understanding Vertices and Coordinates

• Formulas for Calculating the Perimeter

• Step-by-Step Calculation Process

• Examples of Different Triangle Types

  • Equilateral Triangle

  • Isosceles Triangle

  • Scalene Triangle

  • Right Triangle

• Practice Problems

• Applications in Real Life

• Common Mistakes to Avoid

• Additional Resources and References