2012 xIMC keystage2-EMIC team Question 6

Square $MNPQ$ lies inside rectangle $ABCD$, with parallel corresponding sides and $AB-BC=7$ cm. The total area of trapezoids $ABNM,CDQP$ is $123$ cm$^2$, while $ADQM,BCPN$ total $312$ cm$^2$. Find the square area.