Triangle Perimeter from Vertices Calculator

Math

Triangle Perimeter from Vertices Calculator — find perimeter given three vertices using the distance formula.

Formula

Distance = √((x₂-x₁)² + (y₂-y₁)²); Perimeter = sum of 3 sides
  • Distance Formula: d = √((x₂-x₁)² + (y₂-y₁)²).
  • Apply to each pair of vertices to find the three side lengths.
  • Perimeter = side₁ + side₂ + side₃.
  • Also calculates triangle area using the coordinate formula.

3-4-5 Right Triangle (0,0), (3,0), (0,4)

Inputs
  • Vertex 1 X: 0
  • Vertex 1 Y: 0
  • Vertex 2 X: 3
  • Vertex 2 Y: 0
  • Vertex 3 X: 0
  • Vertex 3 Y: 4

Side 1: 3, Side 2: 5, Side 3: 4. Perimeter = 12; Area = 6.

Frequently asked questions

What's the distance formula?
Distance between (x₁,y₁) and (x₂,y₂) is √((x₂-x₁)² + (y₂-y₁)²). It's derived from the Pythagorean theorem.
How do I find the triangle area from vertices?
Use the coordinate formula: Area = |x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)| / 2.
Can I enter 3D coordinates?
This calculator works with 2D (x,y) coordinates. For 3D, use the distance formula: √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²).
What if the vertices are collinear?
If the three points lie on the same line, they don't form a triangle. The calculator will show area = 0.