2018 AMC 12B Problem #20

Geometry Level 3

Let A B C D E F ABCDEF be a regular hexagon with side length 1. Denote by X , X, Y , Y, and Z Z the midpoints of sides A B , \overline{AB}, C D , \overline{CD}, and E F , \overline{EF}, respectively. What is the area of the convex hexagon whose interior is the intersection of the interiors of A C E \triangle ACE and X Y Z \triangle XYZ ?

This problem is part of the 2018 AMC 12B .
1 2 3 \dfrac{1}{2}\sqrt{3} 9 16 3 \dfrac{9}{16}\sqrt{3} 3 8 3 \dfrac{3}{8}\sqrt{3} 7 16 3 \dfrac{7}{16}\sqrt{3} 15 32 3 \dfrac{15}{32}\sqrt{3}

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