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## 'Poly-puzzle' printed from http://nrich.maths.org/

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This rectangle is cut into five pieces which fit exactly into a
triangular outline and also into a square outline where the
triangle, the rectangle and the square have equal areas.

Can you cut up any triangle, using straight cuts, and rearrange
the pieces to make a rectangle and a square?

Start by just investigating triangles which have a height of less
than twice the base but greater than half the base. Make your own
puzzle from card by cutting the triangle into a small number of
pieces that can be re-arranged into a rectangle and into a square
with the same area.

Suppose you have two triangles with the same area. Do you think
you can cut one into pieces which can be re-arranged to form the
other?