Question

How many squares of ANY SIZE can you get from a 6 by 6 grid?

Answer 1

Here, we are given a 6 by 6 grid.

Let's determine the number of squares of ANY SIZE you can get from a 6 by 6 grid.

Let's take n to be one side of the different sizes of square formed.

We have the square as n x n

Where n = 6

Thus, to find the number of squares, we have the formula:

`(n(n+1)(2n+1))/(n)`

Input 6 for n in the expression above:

`\begin{gathered} (6(6+1)(2(6)+1))/(6) \\ \end{gathered}`

Apply distributive property:

`\begin{gathered} ((36+6)(12+1))/(6) \\ \\ =((42)(13))/(6) \\ \\ =(546)/(6) \\ \\ =91 \end{gathered}`

Therefore, we can get 91 squares of ANY SIZE from a 6 by 6 grid

ANSWER:

91