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Question Number 183174 by Mr.D.N. last updated on 22/Dec/22

$$\mathrm{In}\mathrm{the}\mathrm{given}\mathrm{figure}\mathrm{E}\mathrm{is}\mathrm{the}\mathrm{mid}\mathrm{point}\mathrm{of}\mathrm{AB}.$$$$\mathrm{IF}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{\Delta }\mathrm{EBF}\mathrm{is}{8\mathrm{cm}}^2.\mathrm{find}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{parallelogram}\mathrm{ABCD}.$$

Commented by mr W last updated on 22/Dec/22

$$answeris\left(C\right)inthegivenfigure.$$

Commented by Frix last updated on 22/Dec/22

$$\mathrm{Simply}\mathrm{construct}\mathrm{the}\mathrm{ellipse}\mathrm{with}e=\mid DF\mid$$$$\mathrm{through}C\mathrm{and}E\mathrm{and}\mathrm{the}\mathrm{parabola}.\mathrm{The}$$$$\mathrm{area}\mathrm{of}\mathrm{their}\mathrm{intersection}\mathrm{is}\mathrm{half}\mathrm{the}\mathrm{area}\mathrm{of}$$$$\mathrm{the}\mathrm{pentagram}{AC}^{\ast }{EF}^{\ast }{H}_2.$$

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