A triangular plate with base $6$ m and height $2$ m is submerged vertically in water such that the highest vertex of the plate is $4$ meters below the surface and the base is horizontal to the surface.

$4$ m

$6$ m

$2$ m

Express the hydrostatic force against one side of the plate as an integral and evaluate it$.($Round your answer to the nearest whole number. Use $9\mathrm{.}8$ m$/$s$2$ for the acceleration due to gravity. Recall that the weight density of water is $1,000$ kg$/$m$3.)$

$$g

$20$

$$dx

$$ N