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2005 AMC 10BProblem 23P21-25~4 minPrint
Quadrilaterals & Polygon AreasApply an identity: SFFT, sum of squares, difference of cubes, VietaSet up the equation/formula and compute; no special trick needed

In trapezoid ABCDABCD we have AB‾\overline{AB} parallel to DC‾\overline{DC} , EE as the midpoint of BC‾\overline{BC} , and FF as the midpoint of DA‾\overline{DA} . The area of ABEFABEF is twice the area of FECDFECD . What is AB/DCAB/DC ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.