A geometry problem by Charuka BandaraGeometry Level pending
\(E\) and \(N\) are points on the sides \(DC\) and \(DA\) of the square \(ABCD\) such that \(AN : ND : DE = 2 : 3 : 4.\) The line through \(N\) perpendicular to \(BE\) cuts \(BE\) at \(P\) and \(BC\) at \(M\). \(AC\) cuts \(MN\) at \(O\) and \(BE\) at point \(S\). What fraction of the area of \(ABCD\) is the area of triangle \(OPS\)?
Give your answer to the first decimal place.