Getting 36 pieces and a total area of 144 the first idea for a construction is a 12x12 square. With standard coloring this can be done by hand solving. Strict coloring is much more difficult but Patrick Hamlyn provided a solution.

The 12x12 square is also a 6-fold replica of the sqaure tetromino and it might be possible to make strictly colored replicas of the other ones. Solutions with standard coloring can be found rather easily by hand solving as shown below. Since the color of the back isn't marked a little work is left for you.

The three 6x8 rectangles are other examples for multiple congruent shapes. The three rectangles are uniformly colored on the back to make the problem not too easy.

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