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Maximization of the Area of a Quadrilateral

Source:

March 3, 2010
geometry

Problem Statement

ABCD ABCD is a square with side of unit length. Points E E and F F are taken respectively on sides AB AB and AD AD so that AE \equal{} AF and the quadrilateral CDFE CDFE has maximum area. In square units this maximum area is: <spanclass=′latex−bold′>(A)</span> 12<spanclass=′latex−bold′>(B)</span> 916<spanclass=′latex−bold′>(C)</span> 1932<spanclass=′latex−bold′>(D)</span> 58<spanclass=′latex−bold′>(E)</span> 23 <span class='latex-bold'>(A)</span>\ \frac12 \qquad <span class='latex-bold'>(B)</span>\ \frac {9}{16} \qquad <span class='latex-bold'>(C)</span>\ \frac{19}{32} \qquad <span class='latex-bold'>(D)</span>\ \frac {5}{8} \qquad <span class='latex-bold'>(E)</span>\ \frac23
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