On a dotted grid, squares of many different sizes can be made by connecting four points on the grid. Below are some examples of the squares that can be made.
Now…it’s easy to calculate the areas of squares oriented like the green one, right? How about the tilted ones? You see what’s happening there…
Note: the spacing between any two adjacent dots (horizontally & vertically) is 1
In a 7*7 dotted grid (given below), can you determine ALL the possible values the area of a square can take?
Can 5 be area of a square in this grid? What about 11?
Can you find a general way to determine if a number can or cannot represent the area of a square in the grid?
Post different ways of thinking about this problem in the comments. Please try to accompany your answers with explanations. You can also email your solutions on firstname.lastname@example.org