Perimeter of a Triangle with Vertices Calculator
Calculate triangle perimeter using coordinate vertices with the distance formula
Enter Triangle Vertices
Vertex A
Vertex B
Vertex C
Triangle Results
Calculation: P = Side AB + Side AC + Side BC
Distance Formula: d = √[(x₂-x₁)² + (y₂-y₁)²]
Example Calculation
Triangle with Vertices
Vertex A: (0, 0)
Vertex B: (3, 4)
Vertex C: (6, 0)
Side Calculations
AB = √[(3-0)² + (4-0)²] = √[9 + 16] = √25 = 5
AC = √[(6-0)² + (0-0)²] = √[36 + 0] = √36 = 6
BC = √[(6-3)² + (0-4)²] = √[9 + 16] = √25 = 5
Perimeter = 5 + 6 + 5 = 16 units
Distance Formula
The distance between two points
• (x₁, y₁) - First point coordinates
• (x₂, y₂) - Second point coordinates
• d - Distance between points
Triangle Properties
Perimeter
Sum of all three sides
Area
Using shoelace formula
Validity
Points must not be collinear
Calculator Tips
Enter coordinates for each vertex
Coordinates can be positive or negative
Decimal values are supported
Check that points form a valid triangle
Understanding Triangle Perimeter with Vertices
What is Triangle Perimeter with Vertices?
When you know the coordinates of a triangle's vertices but not the side lengths, you need to calculate the perimeter using the distance formula. This method is essential in coordinate geometry and analytical geometry.
Why Use the Distance Formula?
- •Calculates exact distances between coordinate points
- •Based on the Pythagorean theorem
- •Works in any coordinate system
- •Provides precise mathematical results
Step-by-Step Process
- 1. Identify the three vertices: A(x₁,y₁), B(x₂,y₂), C(x₃,y₃)
- 2. Calculate side AB using: √[(x₂-x₁)² + (y₂-y₁)²]
- 3. Calculate side AC using: √[(x₃-x₁)² + (y₃-y₁)²]
- 4. Calculate side BC using: √[(x₃-x₂)² + (y₃-y₂)²]
- 5. Add all three sides for the perimeter
Important: Make sure the three points are not collinear (don't lie on the same straight line), otherwise they won't form a triangle.
Applications
Computer Graphics
Calculating perimeters of triangular shapes in 2D graphics and game development
Engineering
Structural analysis and design calculations for triangular components
Geography
Measuring triangular land areas and boundaries using coordinate systems