Work out shoelace formula area instantly with clear inputs, formula shown and shareable results.
The shoelace (surveyor's) formula sums the cross products of consecutive vertices: A = ½|Σ(xₖyₖ₊₁ − xₖ₊₁yₖ)|. It works for any simple polygon, convex or not, as long as the vertices are given in order around the boundary.
Shoelace formula
A = ½|Σₖ (xₖ·yₖ₊₁ − xₖ₊₁·yₖ)|, wrapping the last vertex to the first
Yes — that is a 4 by 3 rectangle, and the shoelace sum returns exactly 12.
The formula assumes a simple, non-self-intersecting outline. Crossing edges cause the signed pieces to cancel and the answer will be wrong.