The diagram shows part of the curve \(y=32x-4x^2-48\) and the line \(AB\). The curve and the line \(AB\) meet the \(x\)-axis at \(A\) and meet again at the point \(B(5,12)\).
The line \(CD\) extended is parallel to the \(y\)-axis and passes through the maximum point of the curve. Find the area of the shaded region.[9]
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