# PDF of area of convex hull of four random points in square

Four points are chosen uniformly and independently from the unit rectangle $(0,1)\times(0,1)$. What is the probability distribution of the area of their convex hull?

See also The PDF of the area of a random triangle in a square. An answer to this question has applications to What is the probability of having a pentagon in 6 points.

• For what it's worth, the area of convex hull of four points is half of the sum of the areas of the four triangles generated by them. I don't know if it helps though. – JiK Oct 24 '16 at 11:15
• @JiK Thanks. That is a very astute observation. – Otherwise Oct 24 '16 at 17:03
• Perhaps slightly relevant: probability of forming a convex quadrilateral. – Lee David Chung Lin Feb 16 at 16:51