A Rectangular Puzzle

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Rectangular Puzzle 1

This puzzle consists of a rectangular shape cut into pieces and reassembled.

The rectangle can be made from any sheet material, paper, card or wood. I made this from sapele with a pine box to fit.

Rectangular Puzzle 2

The suprising thing is that there are two ways to reassemble it but one of them clearly results in a large piece going 'missing'.

Even with a good maths. education, It takes a while to figure out where the missing piece goes. The thing that particuarly appeals to me is that the 'mathematical error' that permits it is tiny, less than the likely inaccuracies in cutting.

Hint: - Ask Pythagoras!

Rectangular Puzzle 2

Here is the cutting plan.

Good luck!