Let {Ri}1≤i≤n be a family of disjoint closed rectangular surfaces with total area 4 such that their projections of the Ox axis is an interval. Prove that there exist a triangle with vertices in i=1⋃nRi which has an area of at least 1.
[Thanks Grobber for the correction] geometryrectangleinequalitiesanalytic geometrygeometry proposed