In a square, the midpoints of its sides were marked and some segments were drawn. There is another square formed in the centre. Find its area, if the side of the square has length \(10\).
The diagonals of the quadrilateral \(ABCD\) intersect at the point \(O\). Prove that \(S_{AOB} = S_{COD}\) if and only if \(BC \parallel AD\).