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Spot rebelling against his leash

Source: AMC 2002 10A Problem 19

February 11, 2008
geometryAMC

Problem Statement

Spot's doghouse has a regular hexagonal base that measures one yard on each side. He is tethered to a vertex with a two-yard rope. What is the area, in square yards, of the region outside of the doghouse that Spot can reach? (A) 2π/3(B) 2π(C) 5π/2(D) 8π/3(E) 3π \text{(A)}\ 2\pi/3 \qquad \text{(B)}\ 2\pi \qquad \text{(C)}\ 5\pi/2 \qquad \text{(D)}\ 8\pi/3 \qquad \text{(E)}\ 3\pi
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