In this exploration you are trying to find the area of the biggest square that will fit on a 5 by 5 dot grid.

Move the sliders to change the size of the squares. You should see that you can create both upright squares and tilted squares.
1. Create your squares off the grid, when you have one that you think will fit on the grid, unselect show area break down and use the select tool to grab and move your square.
Find all 8 squares with different areas that fit on the 5 by five dot grid. For each square you find record it's area and the vertical and horizontal slider positions that you used to create it.
Notice that if you check show area break down you'll see squares and triangles that you can add up to find the total area. You cannot move the square off and on the 5 by 5 dot grid with show area break down on.