A rectangle with given side lengths is folded back and forth such that the corner touches the opposite side as shown. What is the minimal shaded fraction?
The sneak peek

A rectangle with given side lengths is folded back and forth such that the corner touches the opposite side as shown. What is the minimal shaded fraction?
Three squares, two of which share a vertex. What is the total area?
A square divided by three line segments. What’s the proportion yellow : purple?
A square with its diagonal and a circle. If red is equal to blue, what’s the angle α?
A triangle with an inscribed triangle. What fraction of the former does the latter cover in terms of lengths a, b, c, d, e and f?
A square with several line segments. What fraction is green?
A right triangle with a red and yellow square attached. Two circular arcs centered in the triangle vertices. What is the area of the orange rectangle in terms of red and yellow?
An equilateral triangle containing a parallelogram, another equilateral triangle and a circular arc that is tangent in its base vertices. What is the proportion pink : blue?
A unit square with an extended side immersed in another square. What is the area of the red triangle?
Four squares, three of which are coloured. What’s the area of the blue one?