Enter the (x, y) coordinates of 3 to 6 vertices and compute area, perimeter, and convexity using the shoelace formula — with every term shown step by step.
A = ½|Σ(xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|
where indices wrap: after vertex n comes vertex 1
Perimeter = Σ √((xᵢ₊₁−xᵢ)²+(yᵢ₊₁−yᵢ)²)
A polygon is convex if all cross products of consecutive edge vectors have the same sign. If any have opposite sign, the polygon is concave (has a "dent").
A tutor can make the shoelace formula intuitive and connect it to everything else you know about area.