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Turkey NMO 2000 1st Round - P17 (Geometry)

Source:

July 25, 2012
geometrytrapezoidarea of a triangle

Problem Statement

What is the largest possible area of a quadrilateral with sides 1,4,7,81,4,7,8 ?
<spanclass=′latex−bold′>(A)</span> 72<spanclass=′latex−bold′>(B)</span> 103<spanclass=′latex−bold′>(C)</span> 18<spanclass=′latex−bold′>(D)</span> 123<spanclass=′latex−bold′>(E)</span> 95 <span class='latex-bold'>(A)</span>\ 7\sqrt 2 \qquad<span class='latex-bold'>(B)</span>\ 10\sqrt 3 \qquad<span class='latex-bold'>(C)</span>\ 18 \qquad<span class='latex-bold'>(D)</span>\ 12\sqrt 3 \qquad<span class='latex-bold'>(E)</span>\ 9\sqrt 5
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