There are other symmetric ways to put four squares of size 1 into a square of size 2 (area 4).
Place each small square against one of the edges of the large square, centered on the edge. The squares will overlap; some parts of the large square will not be covered. But it's nice and symmetric. Draw the same design in each of the small squares.
Similarly, place a corner of each small square -- diamond -- on the midpoint of each edge of the large square.
The other way, obvious, is to divide the square orthogonally into 4.
(A solution in search of a problem?)
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