Overlapping Figures

 The Problem :

 An equilateral triangle is put down upon a congruent equilateral triangle so that O is a vertex of one triangle and the centre of the other.  There is an area where the two triangles overlap.  What possible fractions of both triangles can be covered by this area?

Repeat the problem for a square, and for a hexagon.

 Which of the regular polygons behave like squares?

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Last modified: June 18, 2007