Floored

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

Pie Cuts

Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).

Getting an Angle

How can you make an angle of 60 degrees by folding a sheet of paper twice?

Terminology

Stage: 3 Challenge Level:

The green triangle is an isosceles triangle while the blue triangle is an equilateral triangle.

Find $a$ in terms of $b$ and $c$.

What can you say about the triangles if $a = b = c$?