OPQR is a square and M, N are the middle points of the sides PQ and...

Taking the coordinates of vertices $O, P, Q, R$ as $( 0, 0 ) , ( a, 0 ) , ( a, a ) , ( 0, a )$,~respectively.

$∴$ The coordinates of $M$ is \left(a, \dfrac{a}{2}\right)$and N is \left(\dfrac{a}{2}, a\right)$

$∴$~Area of& \Delta OMN = \dfrac{1}{2}\left|\begin{cases}0 & 0 & 1 \\ a & a / 2 & 1 \\ a / 2 & a & 1\end{cases}\right| = \dfrac{3a^{2}}{8}

and area of the square $= a^{2}$

$∴$ The required ratio is $8: 3$.

Hence, option (c) is correct.