Floor Tile Pattern
Source:
January 15, 2009
geometry
Problem Statement
An -foot by -foot floor is tiled with square tiles of size foot by foot. Each tile has a pattern consisting of four white quarter circles of radius 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] (A)\ 80\minus{}20\pi \qquad
(B)\ 60\minus{}10\pi \qquad
(C)\ 80\minus{}10\pi \qquad
(D)\ 60\plus{}10\pi \qquad
(E)\ 80\plus{}10\pi