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How Big?

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

Hex

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

Overlap

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the blue square.

Triangular Tantaliser

Age 11 to 14
Challenge Level

Is there a systematic way that you could work that would ensure you don't miss any triangles?

You could start with certain limitations (constraints) and exhaust all possibilities - try to justfy how you know there are no other triangles in this "category".

Then extend your investigation to more categories.