How Would You Determine How Many Squares Are in a 6X6 Grid?


Finding the number of squares in any given grid can be a daunting task because the squares can be of many sizes. Fortunately, you can use mathematical formulas to find the answer as long as the grid is the same size on every side. To find the total number of squares, use the formula n (2n + 1) (n + 1) / 6, where "n" is the number of units on each side of the grid. You can also find the number of different-size squares by thinking through all the possibilities.

  • Find the number of 1-by-1 squares. For a 6-by-6 grid, you would multiply 6 by 6 to get 36.

  • Find the number of 2-by-2 squares. You can try to count them by hand, but its is easier to use the mathematical formula (n - 1) x (n - 1), where "n" equals the length of each side. You calculate (6 - 1) x (6 - 1), or 5 times 5, to get a result of 25.

  • Find the number of 3-by-3 squares. Multiply (n - 2) x (n - 2), or 4 times 4, to get a result of 16.

  • Find the number of 4-by-4 squares. Multiply (n - 3) x (n - 3), or 3 times 3, to get a result of 9.

  • Find the number of 5-by-5 squares. Multiply (n - 4) x (n - 4), or 2 times 2, to get a result of 4.

  • Find the number of 6-by-6 squares. Multiply (n - 5) x (n - 5), or 1 times 1, to get a result of 1.

  • Add up your results to get the total number of squares in a 6-by-6 grid. Add 36, 25, 16, 9, 4 and1 to get a total of 91 squares.

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