Due to a mistake in the original wording, everyone will receive free points for this problem. There will be no penalty for this problem. Sorry about the inconvenience.
A square is inscribed in a ellipse with equation \(\frac{x^2}{16}+\frac{y^2}{9}=1\). Let the area of intersection of the square inscribed in the ellipse and the rhombus formed when the endpoints of the minor axis and major axis is connected be \(a\). If \(a\) can be expressed as \(\frac{m}{n}\) such that \(m\) and \(n\) are relatively prime, find \(m+n\).