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 direction of $\theta$ is anticlockwise, then $\triangle ABC$ is defined as having positive area.

If the direction of $\theta$ is clockwise, then $\triangle ABC$ is defined as having negative area.

Triangle $\triangle ABC$ with Positive Area

Triangle $\triangle ABC$ with Negative Area

Also see

• Equivalence of Definitions of Sign of Area of Triangle

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text I$. Coordinates: $7$. Sign of an area