Problem

Source: 2006 Romania JBMO TST 1.2

Tags: geometry, combinatorial geometry, combinatorics, triangle area, area, trapezoid



In a plane $5$ points are given such that all triangles having vertices at these points are of area not greater than $1$. Show that there exists a trapezoid which contains all point in the interior (or on the sides) and having the area not exceeding $3$.