MathDB
Hexagon/Square Geo

Source: 2022 AMC 10A #5

November 11, 2022
AMCAMC 102022 AMC 10a2022 AMCgeometrysquare

Problem Statement

Square ABCDABCD has side length 11. Point PP, QQ, RR, and SS each lie on a side of ABCDABCD such that APQCRSAPQCRS is an equilateral convex hexagon with side length ss. What is ss?
<spanclass=′latex−bold′>(A)</span>23<spanclass=′latex−bold′>(B)</span>12<spanclass=′latex−bold′>(C)</span>2−2<spanclass=′latex−bold′>(D)</span>1−24<spanclass=′latex−bold′>(E)</span>23<span class='latex-bold'>(A) </span> \frac{\sqrt{2}}{3} \qquad <span class='latex-bold'>(B) </span> \frac{1}{2} \qquad <span class='latex-bold'>(C) </span> 2-\sqrt{2} \qquad <span class='latex-bold'>(D) </span> 1-\frac{\sqrt{2}}{4} \qquad <span class='latex-bold'>(E) </span> \frac{2}{3}
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