Area of a Triangle Calculator

Visualize and calculate the area of a triangle using vertex coordinates. Get interactive graphs and easy-to-copy results!

Enter Coordinates

Input the x and y coordinates for each vertex of the triangle.

Vertex 1 (A)

Vertex 2 (B)

Vertex 3 (C)

Result

Area of Triangle: square units

Formula used:

`$$Area = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$$`

Triangle Visualization

Understanding Area of a Triangle by Coordinates

The area of a triangle with vertices at points $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ can be calculated using the coordinate formula. This formula is derived from the concept of the determinant of a matrix formed by the coordinates, which geometrically represents the area. The absolute value ensures the area is positive regardless of vertex order. This tool simplifies this calculation and provides a visual representation, making it easier to understand geometric concepts and verify manual calculations. It's widely used in geometry, surveying, and computer graphics.

Formula: $ Area = \frac12 |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| $
Use Cases: Calculating land area, verifying geometric problems, computer graphics rendering.
Related Concepts: Determinants, vector cross product (in 2D), coordinate geometry.