The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.

What is the total area of the first two triangles as a fraction of
the original A4 rectangle? What is the total area of the first
three triangles as a fraction of the original A4 rectangle? If you
could you go on adding all the triangles' areas, what do you think
the total would be as a fraction of the original A4 rectangle?

Can You Explain Why?

Age 11 to 14 Challenge Level:

Imagine having a pencil, ruler, protractor and compass and being
asked to draw the triangle below.

Can you explain why it is an impossible triangle to
construct?