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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?
This problem is copyrighted by the American Mathematics Competitions.
Instructions for entering answers:
- Reduce fractions to
lowest terms and enter in the form 7/9.
- Numbers involving pi should be written as 7pi or 7pi/3
- Square roots should be written as sqrt(3),
5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
- Exponents should be entered in the form 10^10.
- If the problem is multiple choice, enter the appropriate
- Enter points with parentheses, like so: (4,5)
- Complex numbers should be entered in rectangular form
unless otherwise specified, like so: 3+4i. If there is no
real component, enter only the imaginary component (i.e. 2i,
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