The area of any triangle formed by points on a 2D plane can be computed using the shoelace formula: `0.5 * |(x1*(y2 - y3) + x2*(y3 - y1) + x3*(y1 - y2))|`. This works in integer coordinates without needing floating-point until the final division.

Use O(n³) brute force over all triples of points, or use the convex hull to reduce candidate points — the maximum area triangle's vertices always lie on the convex hull of the point set.

Collinear triples produce zero area — skip them. If fewer than 3 non-collinear points exist, return 0.