Problem of the Week
Problem D
The Area Within

Quadrilateral \(ABCD\) is constructed as follows:

• vertex \(A\) is located at the origin;

• vertex \(C\) is at the intersection point of the lines \(\ell_1:~ 5x+2y=30\) and \(\ell_2:~ x+2y=22\);

• vertex \(B\) is at the intersection point of the \(y\)-axis and \(\ell_2\); and

• vertex \(D\) is at the intersection point of the \(x\)-axis and \(\ell_1\).

Determine the area of \(ABCD\).