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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?

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Getting an Angle

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

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Arclets Explained

This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.

Polygon Pictures

Age 11 to 14 Challenge Level:
Start by writing down all the angle facts and rules you can think of that might be useful.
What do you know about the angles in regular polygons?
What shapes are formed by the overlaps?