Take three unit squares made of paper.
Select one of the diagonals of each square and rearrange the squares so the three selected diagonals form
an equilateral triangle with side length equal to the square root of 2.
The outline of all the paper now forms an irregular hexagon (three angles of which are 90 degrees).
Find the area of this irregular hexagon, and find the percentage of area which is one layer of paper, vs two layers, vs three layers.
What is the shape of the region which is three layers?