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2001 AMC 10 Problem 18

Problem 18 of 25IntermediateAlgebraGeometry

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

Consider a repeating 3×33\times3 block of nine small squares. Four of these nine squares are not part of the pentagons, so the pentagons cover 149=5955.6%1-\dfrac49=\dfrac59\approx55.6\% of the area. This is closest to 56.56. Thus, the correct answer is D.

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Concepts: area ratio · tiling · percentage

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.