Water is filled to height H behind a dam of width w. The resultant force on dam is ?

We know that pressure varies with height , so average pressure Pavg =Ptop +P bottom2=0+ρgH2=ρgH2Total force on the dam is ;F=PavgAF=ρgH2×HwF=ρgH2w2

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the answer is 1/2density*g*w*h but how ?
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