60
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96 rectangles.
seven
In a 4 by 4 grid, there are 16 squares (1x1 squares), 9 rectangles that are 2x1, 6 rectangles that are 3x1, 4 rectangles that are 2x2, and 1 rectangle that is 4x4. Therefore, in total, there are 16 squares and 20 rectangles in a 4 by 4 grid.
10
Just four rectangles comprise 64 squares of the same size: 1X64, 2X32, 4X16, and 8X8.