A square is inscribed in the ellipse \(\frac{x^2}{3} + \frac{y^2}{6} = 1,\) so that its sides are parallel to the coordinate axes. Find the area of the square.
The corners of the square are
\(\left(\pm \dfrac s 2, \pm \dfrac s 2\right) so \\ \dfrac{s^2}{12}+\dfrac{s^2}{24}=1\\ 3s^2 = 24 \\ s^2 = 8 =\text{ area of the square}\)
