Polygons inscribed in a square
Source: Bosnia and Herzegovina TST 2012 Problem 6
May 20, 2012
geometrycombinatorics proposedcombinatorics
Problem Statement
A unit square is divided into polygons, so that all sides of a polygon are parallel to sides of the given square. If the total length of the segments inside the square (without the square) is (where is a positive real number), prove that there exists a polygon whose area is greater than .