A square with area is divided into two grey and two transparent squares, each having an area of size ; see the left figure. Another such square is put on top of this square. The side of the second square is lying exactly on the middle of the diagonal of the first square; see the right figure.
What is the area of the grey part in the right figure? Give your answer as a reduced fraction.
Junior Mathematical Olympiad
Solution
Want a route through all this instead of an archive? The track
puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.