Consider the following diagram the point C can be anywhere in the shaded region.
Lets take two extreme cases when the point C is 2,0 and when point C is 2,4. Now I know it is said that point c is p,q and p is less than 0 but we can select p = 1.99999999999 which is almost equal to 2 and q as 3.99999.
In the first case the area of the triangle is = base \(\frac{1}{2}\times\)\(\times\) height = \(\frac{1}{2} \times BC \times\) perpendicular distance of point A from BC = \(\frac{1}{2} \times 4 \times 6 =12\).
In the second case where point C is 2,4 length of BC is 0. So the area of the triangle is almost 0.
Clearly the area of triangle can go higher than 11.2 and as low as 0.
Hence all options are correct!
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