Puzzle Booklet - a2 + b2 = c2

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Time
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Category: 2D Packing Assembly
Description
One of a series of booklets produced in Hungary by hand in limited editions; their contents are made of laser cut wood.
The Hungarian mathematician Farkas Bolyai proved that any two polygons with the same area can be dissected into each other. This puzzle beautifully shows an extension of this theorem. Here, two polygons are dissected into one.

Reference: Greg N. Frederickson, Dissections: Plane & Fancy
Goal
The first goal is to fill the two squares with all 5 pieces.
The second goal is to fit all the pieces into the square hole.
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Craftsman Quality, Limited Production
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