AMC 12 2005b Problem 5

An $8$-foot by $10$-foot floor is tiled with square tiles of size $1$ foot by $1$ foot. Each tile has a pattern consisting of four white quarter circles of radius $1/2$ foot centered at each corner of the tile. The remaining portion of the tile is shaded. How many square feet of the floor are shaded?

unitsize(2cm);
defaultpen(linewidth(.8pt));
fill(unitsquare,gray);
filldraw(Arc((0,0),.5,0,90)--(0,0)--cycle,white,black);
filldraw(Arc((1,0),.5,90,180)--(1,0)--cycle,white,black);
filldraw(Arc((1,1),.5,180,270)--(1,1)--cycle,white,black);
filldraw(Arc((0,1),.5,270,360)--(0,1)--cycle,white,black);

$\mathrm{(A)}\ 80-20\pi \mathrm{(B)}\ 60-10\pi \mathrm{(C)}\ 80-10\pi \mathrm{(D)}\ 60+10\pi \mathrm{(E)}\ 80+10\pi$