Selena draws square \(ABCD\) with side length \(16\) cm. Endre then draws \(\triangle AED\) on top of square \(ABCD\) so that
sides \(AE\) and \(DE\) meet \(BC\) at \(F\) and \(G\), respectively, and
the area of \(\triangle AED\) is twice the area of square \(ABCD\).
Determine the area of trapezoid \(AFGD\).