Calculadora de Área do Triângulo por Coordenadas

This calculator determines the area of a triangle given the Cartesian coordinates of its three vertices. It uses the shoelace formula (or coordinate area formula), which computes the area as half the absolute value of the sum of cross products of the coordinates. Simply enter the ordered pairs (x, y) for each point and the result will be displayed in square units.

How it works: the formula A = |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)| / 2 is applied automatically. The absolute value ensures the area is always positive regardless of point order. This calculation is useful in analytic geometry, computer graphics, surveying, and physics, where you need the area of triangular regions defined by points on a plane.

When to use? For example, when working with maps or engineering projects, if you know the coordinates of a triangular plot's vertices, you can directly compute its area. It is also helpful for verifying areas in graphs, solving geometry problems, or programming algorithms involving polygons. Avoid using this calculator if the points are collinear, as the area will be zero and the triangle does not exist.

Cautions: enter coordinates correctly, using a period for decimals (e.g., 3.5). The order of points does not affect the result, but the formula assumes the three points are distinct and non-collinear. If you get zero area, check if the points are aligned. The calculator does not validate whether the points form a valid triangle, so the user must ensure that.