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2001 AMC 10Problem 24P21-25~4 minPrint
Triangles: Area & PythagoreanAlgebraic ManipulationQuadrilaterals & Polygon AreasApply an identity: SFFT, sum of squares, difference of cubes, VietaAdd construction lines/points (drop altitudes, extend segments, connect centers)

In trapezoid ABCDABCD , AB‾\overline{AB} and CD‾\overline{CD} are perpendicular to AD‾\overline{AD} , with AB+CD=BCAB+CD=BC , AB<CDAB<CD , and AD=7AD=7 . What is AB⋅CDAB\cdot CD ?

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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.