Double Crosses

Geometry Level 3

The line \(l_{1} : y = \dfrac{3}{2}x - 6\) is perpendicular to the line \(l_{2}\), where the \(x\)-intercept of \(l_{2}\) is at point \((10.5 , 0)\).

Let point \(A\) be the intersection of both lines, point \(B\) be the \(x\)-intercept of \(l_{1}\), point \(C\) be the \(y\)-intercept of \(l_{2}\), and point \(O\) be the point of origin \((0 , 0)\).

What is the area of the quadrilateral \(ABOC\)?

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