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Oh, that's a happy little question! In a 6x6 grid, you have 36 individual squares. But if you count all the different sizes of squares that can fit within the grid, including the whole grid itself, you have a total of 91 squares to enjoy painting with your imagination.
There are 49 of the smallest squares. However, any grid forms "squares" that consist of more than one of the smallest squares. For example, there are four different 6x6 squares that each include 36 of the small squares, nine different 5x5 squares, sixteen 4x4 squares, twenty-five 3 x 3 squares, and thirty-six different squares that contain 4 of the small squares. One could therefore discern 140 distinct "squares." The number can be calculated from the formula [(n)(n+1)(2n+1)] / 6 where n is the grid size.
Take the product of the dimensions to solve this: 6 x 6 = 36 So your answer is 36 squares.
441
To calculate the number of rectangles in a 5 by 4 grid, you can use the formula for the number of rectangles in an n by m grid, which is n*(n+1)m(m+1)/4. Plugging in the values for n=5 and m=4, you get 5*(5+1)4(4+1)/4 = 564*5/4 = 600/4 = 150 rectangles. So, there are a total of 150 rectangles in a 5 by 4 grid.