Try this with a trapezium instead
Let \(S\) be the set of lattice points \((x,y)\) with \( 1 \leq x \leq 20 \) and \( 1 \leq y \leq 30. \) Let \(B \subseteq S\) be a subset of \(S\) such that no set of \(4\) vertices in \(B\) form a (non-degenerate) parallelogram. What is the largest possible number of elements in \(B?\)
Details and assumptions
A figure is degenerate if it has 0 area.