Some solution we were offered cleverly
reasoned that the grid, offered in the Hint as an approximation,
was in fact completely accurate at the pixel level - which for
printer ink is what counts. Sometimes we explore mathematics in
unreal perfection for the sake of the thinking that will draw us
into. Other solutions did this:

"You can split the problem up into combinations of circular shapes, each of which we can find the area of. Doing this I foundthat the star is over 5% larger than the S shape."