Definition:Sign of Area of Triangle/Definition 1

Definition
Let $\triangle ABC$ be a triangle embedded in the plane.

Let $\theta$ be the angle between $AB$ and $AC$.

If the [Definition:Angle/Directed versus Undirected|direction]] of $\theta$ is anticlockwise, then $\triangle ABC$ is defined as having positive area.

If the [Definition:Angle/Directed versus Undirected|direction]] of $\theta$ is clockwise, then $\triangle ABC$ is defined as having negative area.


 * Positive-triangle.png


 * Triangle $\triangle ABC$ with Positive Area


 * Negative-triangle.png


 * Triangle $\triangle ABC$ with Negative Area

Also see

 * Equivalence of Definitions of Sign of Area of Triangle