# Unfold a right angle pyramid into a square

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?

• Comments are not intended for discussion - and particularly not for discussion of an entirely different question. If you want to discuss a question's closure, try asking about it on our Puzzling Meta. – Rubio Jul 17 at 0:21
• Can you define "right angle pyramid" for me, please? – Dr Xorile Sep 5 at 18:23
• Very similar to this question: puzzling.stackexchange.com/questions/86082/… – Dr Xorile Sep 5 at 18:26
• Similar but not the same. – Moti Sep 6 at 19:14