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

In the given figure E is the mid point of AB. IF the area of ΔEBF is 8cm^2 .find the area of the parallelogram ABCD.

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

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

answer is (C) in the given figure.

$${answer}\:{is}\:\left({C}\right)\:{in}\:{the}\:{given}\:{figure}. \\ $$

Commented by Frix last updated on 22/Dec/22

Simply construct the ellipse with e=∣DF∣ through C and E and the parabola. The area of their intersection is half the area of the pentagram AC^∗ EF^∗ H_2 .

$$\mathrm{Simply}\:\mathrm{construct}\:\mathrm{the}\:\mathrm{ellipse}\:\mathrm{with}\:{e}=\mid{DF}\mid \\ $$$$\mathrm{through}\:{C}\:\mathrm{and}\:{E}\:\mathrm{and}\:\mathrm{the}\:\mathrm{parabola}.\:\mathrm{The} \\ $$$$\mathrm{area}\:\mathrm{of}\:\mathrm{their}\:\mathrm{intersection}\:\mathrm{is}\:\mathrm{half}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{pentagram}\:{AC}^{\ast} {EF}^{\ast} {H}_{\mathrm{2}} . \\ $$

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