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geometry intermediate

Problem

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)
(B)
(C)
(D)
(E)
Solution
Part of what Spot can reach is of a circle with radius 2, which gives him . He can also reach two parts of a unit circle, which combines to give . The total area is then , which gives .
Final answer
E