Triangle Area Calculator by Coordinates

Calculate triangle area, perimeter, and properties using 2D coordinate geometry

Triangle Coordinates
Enter the coordinates of the three vertices

Point A

Point B

Point C

Triangle Properties
Calculated properties based on the coordinates

Enter valid triangle coordinates to see the properties

Make sure the three points don't lie on a straight line

Triangle Area Calculation Using Coordinates

Coordinate Geometry for Triangles

When you know the coordinates of a triangle's vertices, you can calculate its area, perimeter, and other properties using coordinate geometry formulas.

Area Formula (Shoelace Method)

For a triangle with vertices at (x₁, y₁), (x₂, y₂), and (x₃, y₃):

Area = ½|x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|

This formula is derived from the cross product and gives the absolute area of the triangle.

Distance Formula

To calculate the length of each side, we use the distance formula between two points:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Centroid Calculation

The centroid is the center point of the triangle, calculated as:

Centroid = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3)

Applications

Engineering

  • Land surveying
  • CAD design
  • Structural analysis

Computer Graphics

  • 3D modeling
  • Game development
  • Animation