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Ratios of Areas Within a Trapezoid

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January 15, 2009
ratiogeometrytrapezoidrectangle

Problem Statement

In trapezoid ABCD ABCD we have AB‾ \overline{AB} parallel to DC‾ \overline{DC}, E E as the midpoint of BC‾ \overline{BC}, and F F as the midpoint of DA‾ \overline{DA}. The area of ABEF ABEF is twice the area of FECD FECD. What is AB/DC AB/DC? <spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 5<spanclass=′latex−bold′>(D)</span> 6<spanclass=′latex−bold′>(E)</span> 8 <span class='latex-bold'>(A)</span>\ 2\qquad <span class='latex-bold'>(B)</span>\ 3\qquad <span class='latex-bold'>(C)</span>\ 5\qquad <span class='latex-bold'>(D)</span>\ 6\qquad <span class='latex-bold'>(E)</span>\ 8
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