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2013 PUMaC Geometry A3

Source:

November 22, 2013
geometryUSAMTSrectangle

Problem Statement

Consider the shape formed from taking equilateral triangle ABCABC with side length 66 and tracing out the arc BCBC with center AA. Set the shape down on line ll so that segment ABAB is perpendicular to ll, and BB touches ll. Beginning from arc BCBC touching ll, we roll ABCABC along ll until both points AA and CC are on the line. The area traced out by the roll can be written in the form nπn\pi, where nn is an integer. Find nn.
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