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Question Number 126052 by fajri last updated on 16/Dec/20

  on any trapezoid ABCD points E and   F are located on CD so that AD is  parallel to BE and AF is parallel to   BC.Point H is the intersection of AF   and BE point G is the intersection of   AC and BE. If the length of AB is 4 cm  and the length of CD is 10 cm what is  the ratio of the area of triangle AGH to  the area of trapezoid ABCD?

$$ \\ $$$$\mathrm{on}\:\mathrm{any}\:\mathrm{trapezoid}\:\mathrm{ABCD}\:\mathrm{points}\:\mathrm{E}\:\mathrm{and}\: \\ $$$$\mathrm{F}\:\mathrm{are}\:\mathrm{located}\:\mathrm{on}\:\mathrm{CD}\:\mathrm{so}\:\mathrm{that}\:\mathrm{AD}\:\mathrm{is} \\ $$$$\mathrm{paral}{l}\mathrm{el}\:\mathrm{to}\:\mathrm{BE}\:\mathrm{and}\:\mathrm{AF}\:\mathrm{is}\:\mathrm{parallel}\:\mathrm{to}\: \\ $$$$\mathrm{BC}.\mathrm{Point}\:\mathrm{H}\:\mathrm{is}\:\mathrm{the}\:\mathrm{intersection}\:\mathrm{of}\:\mathrm{AF}\: \\ $$$$\mathrm{an}{d}\:\mathrm{BE}\:\mathrm{point}\:\mathrm{G}\:\mathrm{is}\:\mathrm{the}\:\mathrm{intersection}\:\mathrm{of}\: \\ $$$$\mathrm{AC}\:\mathrm{and}\:\mathrm{BE}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{AB}\:\mathrm{is}\:\mathrm{4}\:\mathrm{cm} \\ $$$${an}\mathrm{d}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{CD}\:\mathrm{is}\:\mathrm{10}\:\mathrm{cm}\:\mathrm{what}\:\mathrm{is} \\ $$$$\mathrm{th}{e}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{triangle}\:\mathrm{AGH}\:\mathrm{to} \\ $$$$\mathrm{t}{h}\mathrm{e}\:\mathrm{area}\:\mathrm{of}\:\mathrm{trapezoid}\:\mathrm{ABCD}? \\ $$

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