phanideepak
Are you by any chance talking about the trapezium in which the 4 points lie within the bounded region??
and if that were the case the answer should be E because we can only find the bounds of the bounded region and not the specific points in that region.
The question and solution are fine.
You have four lines: x axis, y axis, y = 6 and y = ax + 8
You need the value of a to get the area bounded by these lines.
Stmnt1: This tells you that (1, 6) lies on the boundary (one of the lines) of the quadrilateral (not that it is a vertex necessarily). We know that y = 6 passes through this point anyway. All this says is that y = 6 intersects with y = ax + 8 at a point (m, 6) such that m is greater than 1. We still do not know the value of a and hence this is not sufficient.
Stmnt2: None of x axis, y axis and y = 6 can pass through (6, 5). If (6, 5) lies on the boundary of the quadrilateral, y = ax + 8 has to pass through it. So we know a point on y = ax + 8 which will give us the value of 'a' and hence the equation of the fourth line. This will give us the area of the quadrilateral. Sufficient
Also, in your figure, the second diagram is not possible because that line cannot pass through (6, 5). Its y co-ordinate will be greater than 8 in the first quadrant.