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We call a set of n points in the Euclidean plane “wide” if at most $$\sqrt{n}$$of its points are collinear. We show that in such sets, the maximum possible number of trapezoids is $$\;\Omega (n^{3}\log n)$$and $$O(n^{3}\log ^2 n)$$while for deltoids we have $$\;\Omega (n^{5/2})$$and $$O(n^{8/3}\log n)$$.

Trapezoids and Deltoids in Wide Planar Point Sets