a) Prove that a>0 exists such that for each natural number n, there exists a convex n-gon P in plane with lattice points as vertices such that the area of P is less than an3.b) Prove that there exists b>0 such that for each natural number n and each n-gon P in plane with lattice points as vertices, the area of P is not less than bn2.c) Prove that there exist α,c>0 such that for each natural number n and each n-gon P in plane with lattice points as vertices, the area of P is not less than cn2+α.Proposed by Mostafa Eynollahzade geometrycombinatorics proposedcombinatorics