Ugh...5:00, time to go, and I get Must-See-TV and sushi tonight.
But in a nutshell, look closely and you'll see that the sloping lines of the quadrilateral are not perfectly straight. (They're quadrilaterals, not triangles.) Furthermore, the lines don't dissect the squares evenly...another way to tell. So, then if you add up the area (total squares covered), both will be the same because you're using two sets of the same geometric shapes. However, they don't connect the same way because of the imperfections of the lines. So, the same area is covered with one big obvious hole (which isn't counted in the area) even though the "shape" of the area covered seems to change because of the big hole.
I hope that makes sense because I can't do the math part here to show you further....no time. Sorry!
ER! Yay!
Bye, Carter!
