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Trapezoidal Diagonals

Source: AMC 10 2008A Problem 20

February 22, 2008
geometrytrapezoidratioAMC

Problem Statement

Trapezoid ABCD ABCD has bases AB‾ \overline{AB} and CD‾ \overline{CD} and diagonals intersecting at K K. Suppose that AB\equal{}9, DC\equal{}12, and the area of △AKD \triangle AKD is 24 24. What is the area of trapezoid ABCD ABCD? <spanclass=′latex−bold′>(A)</span> 92<spanclass=′latex−bold′>(B)</span> 94<spanclass=′latex−bold′>(C)</span> 96<spanclass=′latex−bold′>(D)</span> 98<spanclass=′latex−bold′>(E)</span> 100 <span class='latex-bold'>(A)</span>\ 92 \qquad <span class='latex-bold'>(B)</span>\ 94 \qquad <span class='latex-bold'>(C)</span>\ 96 \qquad <span class='latex-bold'>(D)</span>\ 98 \qquad <span class='latex-bold'>(E)</span>\ 100
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