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AMC10 2027 - Self-practice Set 7 Question 2

AMC10 · AMC10 2027 - Self-practice Set 7

Question 2

Let $ABCDEF$ be a regular hexagon with side length $1.$ Denote by $X,$ $Y,$ and $Z$ the midpoints of sides $AB,$ $CD,$ and $EF,$ respectively. What is the area of the convex hexagon whose interior is the intersection of the interiors of $\triangle ACE$ and $\triangle XYZ?$
  1. $\dfrac{3}{8}\sqrt{3}$
  2. $\dfrac{7}{16}\sqrt{3}$
  3. $\dfrac{15}{32}\sqrt{3}$
  4. $\dfrac{1}{2}\sqrt{3}$
  5. $\dfrac{9}{16}\sqrt{3}$