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2001 AMC 12 Problem 10

Problem 10 of 25EasierGeometryCombinatoricsArithmetic

The plane is tiled by congruent squares and congruent pentagons as indicated. The percent of the plane that is enclosed by the pentagons is closest to

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Solution

The pattern repeats over a 3×33 \times 3 block of nine unit squares. Four of these nine squares are not covered by pentagons; the rest of the area belongs to the pentagons. So the pentagons enclose 1−49=59=55.55‾%, 1 - \dfrac{4}{9} = \dfrac{5}{9} = 55.5\overline{5}\%, which is closest to 56.56. Thus, the correct answer is D.
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Tagged: tiling · area · percentage

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