This puzzle refers to a feature of right angle pyramid:

The relation between the areas of the three perpendicular faces and the diagonal surface area is given as - $S^2_x+S^2_y+S^2_z = S^2_d$

Visit the link for details: De Gua's theorem

  1. The challenge is to unfold the 3D pyramid surfaces into a 2D shape and than cut it into two pieces to be reassembled into a square. There is one specific case where unfolding will create a square with no need to cut the shape.

  2. It is not possible for all pyramids (I think) - what is the condition with regard to the surfaces for this to be solved?

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