Question 2
A2 (YUG 1). Let $K$ be a convex polygon in the plane and suppose that $K$ is positioned in the coordinate system in such a way that
$$\operatorname{area}(K\cap Q_i)=\frac14\operatorname{area}K\quad(i=1,2,3,4,),$$
where the $Q_i$ denote the quadrants of the plane. Prove that if $K$ contains no nonzero lattice point, then the area of $K$ is less than 4.
$$\operatorname{area}(K\cap Q_i)=\frac14\operatorname{area}K\quad(i=1,2,3,4,),$$
where the $Q_i$ denote the quadrants of the plane. Prove that if $K$ contains no nonzero lattice point, then the area of $K$ is less than 4.