sides of parallelogram are diagonals of 4 squares
Source: IV Soros Olympiad 1997-98 Corr. 11.5 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
June 1, 2024
geometryparallelogramareas
Problem Statement
The sides of the parallelogram serve as the diagonals of the four squares. The vertices of the squares lying in the part of the plane external to the parallelogram (the sides of the squares emerging from these vertices do not have common points with the parallelogram) serve as the vertices of a quadrilateral of area , the four vertices opposite to them form a quadrilateral of area . Find the area of the parallelogram.