Data Sufficiency

stmnt 1:
ABC= 30
=> the other two angles 60 and 90.
and we do know one side, so we could fetch the area.
Sufficient

Stmnt 2:
circumference = 18pi.
=> radius, r= 9.
We do know one side, i.e; 18= AB, which could act as the base of the triangle, and the perpendicular dropped from AB would be the height of the triangle.
Thus we could get the area in this way too.

Thus, answer is D.

But it's not the OA?
Why's it so?
OA would be provided once you give your explanations.

statement 1:

even though it looks as if it is a right triangle it is not stated anywhere.
It doesn't even say that the line AB goes through the center of the circle.

You cannot assume anything like that and those graphics are often misleading.

Therefore not enough information: INSUFFICIENT

statement 2:
circumference = 18pi ---> 2pi*r ---> r=9
we then know that AB is the diameter of the circle (=18)
Any traingle formed with the diameter and any point of the circle is a 90-degree-triangle.
But only the hypothenuse does not help in determining the area of the triangle.

Therefore not enough information: INSUFFICIENT

Take both statements together:
It is a 30-60-90 triangle.
We know one side and can calculate according to the ratios of the lengths of the sides first the lengths of those other sides and then the area.

Answer C

Now that's fast math, and it's correct btw.