# Problem #2158

 2158 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? $[asy]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);[/asy]$$\textrm{(A)}\ 80-20\pi \qquad \textrm{(B)}\ 60-10\pi \qquad \textrm{(C)}\ 80-10\pi \qquad \textrm{(D)}\ 60+10\pi \qquad \textrm{(E)}\ 80+10\pi$ This problem is copyrighted by the American Mathematics Competitions.
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