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Parrallelogram => Quadrilateral

Source: 1964 AHSME Problem 22

August 23, 2013
geometryparallelogramratiotrigonometryAMC

Problem Statement

Given parallelogram ABCDABCD with EE the midpoint of diagonal BDBD. Point EE is connected to a point FF in DADA so that DF=13DADF=\frac{1}{3}DA. What is the ratio of the area of triangle DFEDFE to the area of quadrilateral ABEFABEF?
<spanclass=′latex−bold′>(A)</span> 1:2<spanclass=′latex−bold′>(B)</span> 1:3<spanclass=′latex−bold′>(C)</span> 1:5<spanclass=′latex−bold′>(D)</span> 1:6<spanclass=′latex−bold′>(E)</span> 1:7 <span class='latex-bold'>(A)</span>\ 1:2 \qquad<span class='latex-bold'>(B)</span>\ 1:3 \qquad<span class='latex-bold'>(C)</span>\ 1:5 \qquad<span class='latex-bold'>(D)</span>\ 1:6 \qquad<span class='latex-bold'>(E)</span>\ 1:7
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