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Hexagon Ratios

Source: Problem #23 2016 AMC 10B

February 21, 2016
AMCAMC 10AMC 10 B2016 AMC 10Bgeometryarea

Problem Statement

In regular hexagon ABCDEFABCDEF, points WW, XX, YY, and ZZ are chosen on sides BC‾\overline{BC}, CD‾\overline{CD}, EF‾\overline{EF}, and FA‾\overline{FA} respectively, so lines ABAB, ZWZW, YXYX, and EDED are parallel and equally spaced. What is the ratio of the area of hexagon WCXYFZWCXYFZ to the area of hexagon ABCDEFABCDEF?
<spanclass=′latex−bold′>(A)</span> 13<spanclass=′latex−bold′>(B)</span> 1027<spanclass=′latex−bold′>(C)</span> 1127<spanclass=′latex−bold′>(D)</span> 49<spanclass=′latex−bold′>(E)</span> 1327<span class='latex-bold'>(A)</span>\ \frac{1}{3}\qquad<span class='latex-bold'>(B)</span>\ \frac{10}{27}\qquad<span class='latex-bold'>(C)</span>\ \frac{11}{27}\qquad<span class='latex-bold'>(D)</span>\ \frac{4}{9}\qquad<span class='latex-bold'>(E)</span>\ \frac{13}{27}
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