An area of a cut

[kate]

The base of a pyramid ABCDM is the distinguishable quadrilateral ABCD with perpendicular diagonals and sides AB = 5, BC = √13, CD = √5, AD = √17. The intersection point of the diagonals is O, which is a projection of M into the plain of the base, and OM = 4√3. The plain α, defined from the middles of the sections AB, AD and OM, concludes a 60^\circ angle with the base. Calculate the area of the cut of the pyramid with the plain α.