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2008 AMC 10A Question 17

AMC10 · 2008 AMC 10A

Question 17

An equilateral triangle has side length $6.$ What is the area of the region containing all points that are outside the triangle and not more than $3$ units from a point of the triangle?
  1. $36 + 24\sqrt{3}$
  2. $54 + 9\pi$
  3. $54 + 18\sqrt{3} + 6\pi$
  4. $\left(2\sqrt{3} + 3\right)^2 \pi$
  5. $9\left(\sqrt{3} + 1\right)^2 \pi$