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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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Convex Polygons

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

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Bow Tie

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

Getting an Angle

Age 11 to 14 Challenge Level:

Remember that folding an equilateral triangle in half gives you a 30-60-90 triangle and the ratios of the lengths of the sides.