AMC 10 Step by Step
2012 AMC 10AProblem 18P16-20~5 minPrint

The closed curve in the figure is made up of 99 congruent circular arcs each of length 2π3\frac{2\pi}{3} , where each of the centers of the corresponding circles is among the vertices of a regular hexagon of side 22 . What is the area enclosed by the curve?

figure

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.