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2016 AMC 10B Question 23

AMC10 · 2016 AMC 10B

Question 23

In regular hexagon $ABCDEF,$ points $W,$ $X,$ $Y,$ and $Z$ are chosen on sides $\overline{BC},$ $\overline{CD},$ $\overline{EF},$ and $\overline{FA}$ respectively, so lines $AB,$ $ZW,$ $YX,$ and $ED$ are parallel and equally spaced. What is the ratio of the area of hexagon $WCXYFZ$ to the area of hexagon $ABCDEF?$
  1. $ \ \dfrac{1}{3} $
  2. $ \ \dfrac{10}{27} $
  3. $ \ \dfrac{11}{27} $
  4. $ \ \dfrac{4}{9} $
  5. $ \ \dfrac{13}{27} $