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2005 AMC 10A Question 12

AMC10 · 2005 AMC 10A

Question 12

The figure shown is called a *trefoil* and is constructed by drawing circular sectors about sides of the congruent equilateral triangles. What is the area of a trefoil whose horizontal base has length $2?$

Question illustration
  1. $\dfrac{1}{3}\pi + \dfrac{\sqrt{3}}{2}$
  2. $\dfrac{2}{3}\pi$
  3. $\dfrac{2}{3}\pi + \dfrac{\sqrt{3}}{4}$
  4. $\dfrac{2}{3}\pi + \dfrac{\sqrt{3}}{3}$
  5. $\dfrac{2}{3}\pi + \dfrac{\sqrt{3}}{2}$