If you think back to when you were 14 (to do this your memory will need to be lot better than mine) you will probably recall that the subject covered immediately before calculus was estimating areas under curves.
Calculus is after all simply a method for estimating areas under curves. Which is why I said in my previous post that, "This method (square counting) is just the poor man’s calculus".
More recently having spent 10 years teaching ATPL theory, I have found that the majority (yes I really do mean the majority) of modern-day ATPL students would stop listening at the very mention of calculus. But even the most mathematically challenged could count squares.