Shoelace Formula
Triangle Area (Counter-Clockwise)
What if we were to switch points and ?
What would happen?
Triangle Area (Clockwise)
Shoelace for Quadrilateral
The formula can also be applied to Quadrilaterals or other polygons in general. Try dragging A,B,C,D around to see what happens if the quadrilateral is not convex, or if it is self-intersecting. Does it seem like the formula is still valid?