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2010 AMC 10AProblem 19P16-20~7 minPrint
Quadrilaterals & Polygon AreasAngles & PolygonsQuadraticsApply an identity: SFFT, sum of squares, difference of cubes, VietaCut the figure into known shapes (triangles, rectangles, sectors)Exploit symmetry to reduce work or pair up objects

Equiangular hexagon ABCDEFABCDEF has side lengths AB=CD=EF=1AB=CD=EF=1 and BC=DE=FA=rBC=DE=FA=r . The area of △ACE\triangle ACE is 70%70\% of the area of the hexagon. What is the sum of all possible values of rr ?

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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.