3.41: Area with curve $y=32x-4x^{2}-48$ and chord

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