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Triangle Madness

Source: 2018 AMC 12B #20

February 16, 2018
AMC 12AMCAMC 12 B2018 AMC 12B2018 AMC

Problem Statement

Let ABCDEFABCDEF be a regular hexagon with side length 11. Denote by XX, YY, and ZZ the midpoints of sides AB‾,CD‾,EF‾\overline{AB},\overline{CD},\overline{EF}, respectively. What is the area of the convex hexagon whose interior is the intersection of the interiors of △ACE\triangle{ACE} and △XYZ\triangle{XYZ}?
<spanclass=′latex−bold′>(A)</span>383<spanclass=′latex−bold′>(B)</span>7163<spanclass=′latex−bold′>(C)</span>15323<spanclass=′latex−bold′>(D)</span>123<spanclass=′latex−bold′>(E)</span>9163<span class='latex-bold'>(A) </span>\dfrac{3}{8}\sqrt{3}\qquad<span class='latex-bold'>(B) </span>\dfrac{7}{16}\sqrt{3}\qquad<span class='latex-bold'>(C) </span>\dfrac{15}{32}\sqrt{3}\qquad<span class='latex-bold'>(D) </span>\dfrac{1}{2}\sqrt{3}\qquad<span class='latex-bold'>(E) </span>\dfrac{9}{16}\sqrt{3}
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