$($Force on plane surface$)$ The rectangular gate $CD$ of the figure below is $1\mathrm{.}9$ m wide and $2\mathrm{.}0$ m long. Assuming the material of the gate to be homogeneous and neglecting friction at the hinge C$,$ determine the weight of the gate necessary to keep it shut until the water level rises to $2\mathrm{.}2$ m above the hinge.

$W=$

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