MathDB
Octagon vs Square

Source: 2020 AMC 12A #14

January 31, 2020
AMCAMC 12AMC 12 Ageometry2020 AMC 12A2020 AMCOctogon

Problem Statement

Regular octagon ABCDEFGHABCDEFGH has area nn. Let mm be the area of quadrilateral ACEGACEG. What is mn?\tfrac{m}{n}?
<spanclass=′latex−bold′>(A)</span>24<spanclass=′latex−bold′>(B)</span>22<spanclass=′latex−bold′>(C)</span>34<spanclass=′latex−bold′>(D)</span>325<spanclass=′latex−bold′>(E)</span>223<span class='latex-bold'>(A) </span> \frac{\sqrt{2}}{4} \qquad <span class='latex-bold'>(B) </span> \frac{\sqrt{2}}{2} \qquad <span class='latex-bold'>(C) </span> \frac{3}{4} \qquad <span class='latex-bold'>(D) </span> \frac{3\sqrt{2}}{5} \qquad <span class='latex-bold'>(E) </span> \frac{2\sqrt{2}}{3}
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