$($Force on plane surface$)$ The rectangular gate $\backslash ($ C D $\backslash )$ of the figure below is $2\mathrm{.}0$ m wide and $2\mathrm{.}0$ m long. Assuming the material of the gate to be homogeneous and neglecting friction at the hinge $\backslash ($ C $\backslash ),$ determine the weight of the gate necessary to keep it shut until the water level rises to $2\mathrm{.}2$ m above the hinge.