I decided to try to and find a pattern because it was getting confusing working out all 10 squares at once. I started at one small rectangle which had 1 rectangle, then I did 2 small rectangles which had three overall rectangles as proved by Max, then 3 small rectangles which had 6 overall rectangles which was also proved by Max, then 4 small rectangles which had 10 overall rectangles (4 little squares, 4 rectangles 2 little rectangles long and 2 more rectangles 3 little rectangles long).
Then when I tried to find a pattern I worked out that it was going up by the previous amount added with this number. But this still didn’t help me if I was trying to find the 100th number, therefore I tried to work out a formula for it.
Then I realised it was the triangle numbers; the formula for working out triangle numbers is if Xn is the number: Xn = n(n+1)/2
So the 10th number is 55
So the 100th number is 5050
So the 1000th number is 500500
And so on forever.