If the length of the semi major axis of an ellipse is 68 and eccentricity is $\frac{1}{2}$then the area of the rectangle formed by joining the vertices of the latusrecta of the ellipse is equal to

$\begin{array}{l}\mathrm{Given} \mathrm{a}=68,\mathrm{e}=\frac{1}{2}\Rightarrow {\mathrm{b}}^2={\mathrm{a}}^2\left(1-{\mathrm{e}}^2\right)\\ Now \Rightarrow {\mathrm{b}}^2={\mathrm{a}}^2\left(1-{\mathrm{e}}^2\right)=3468\\ Therefore area of the rec\tan gle formed by joining latus rectum as length=\frac{2b^2}{a} \\ and breadth is the dis\tan ce between the latus rectum=2ae\\ \Rightarrow \text{ Area }=\frac{2\times 3468\times 68}{68}=6936\end{array}$