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Problem of the Week
Problem D
Shading the Quad

Peggie draws the line \(3x+4y=48\) and labels its intersection with the \(y\)-axis \(A\). Derrick then draws the line \(x+2y=22\) on the same set of axes and labels its intersection with Peggie’s line \(B\). Derrick then labels the intersection of his line with the \(x\)-axis \(C\). Peggie then labels the origin \(D\) and shades in quadrilateral \(ABCD\), as shown.

The two lines and quadrilateral ABCD plotted on the Cartesian plane. Point A is on the positive y-axis, point C is on the positive x-axis, and point B is in the first quadrant to the right and below point A and to the left and above point C.

Determine the area of quadrilateral \(ABCD\).