Área Triângulo (vetorial 2D)

The 2D vector triangle area calculator determines the area of a triangle from the Cartesian coordinates of its three vertices. It uses the shoelace formula (or coordinate area formula), widely used in analytic geometry. The calculation is done through the absolute value of half the determinant formed by the coordinates of the points, resulting in a positive number representing the area. This tool is useful for students and professionals who need a quick and accurate result without manual calculations.

How it works: simply enter the x and y coordinates of each vertex (A, B, and C) in the corresponding fields. The calculator applies the formula: Area = ½ · |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|. The result is displayed in square units, according to the unit of the provided coordinates. The formula derives from the 2D cross product, where the area is half the magnitude of the cross product of two side vectors.

When to use? This calculator is ideal for solving analytic geometry problems, such as determining areas of planar figures in coordinate systems, checking school exercise results, or in applications of computer graphics and engineering involving triangulation. It is also useful for verifying manual calculations or when vertices are given in decimal or fractional coordinates.

Cautions: Make sure the coordinates are correct and in the expected order (A, B, C). The formula assumes the points are not collinear; if they are, the area will be zero. Also, the result is always positive, as the formula uses absolute value. Remember that the area unit is the square of the coordinate unit (e.g., if coordinates are in meters, area is in square meters).