[Math] How many different rectangles (in terms of area) can fit in a 20-unit-wide square

Question

How many different rectangles (in terms of area) can fit in a 20-unit-wide square? The rectangles can be squares, and their dimensions are integers.

Answer 1

If you're looking for the number of different areas realizable by fitting rectangles in a 20x20 square with (integer-length) edges parallel to the coordinate axes, the answer is the number of elements in {$ \{ x \times y | x,y \in \{ 1..20 \} \} $}. In Haskell, length . List.nub . sort $ [x*y| x<-[1..20] , y<-[1..20]] evaluates to 152.