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Dividing into 4 identical shapes

I am going to describe here a logical puzzle which involves dividing  a given shape into 4 identical shapes.

Problem 1: Draw a square. Divide it into 4 identical squares. Remove the bottom left square and divide the resulting shape into 4 identical shapes.

Problem 2: Draw an equilateral triangle. Divide it into 4 identical shapes. Now, remove the bottom leftmost shape and divide the resulting shape into 4 identical shapes.

Solution