In the figure above, what is the area of the shaded region?

It might be wrong, but...do we know that O is the center to conclude that OA=OB ?

I Agree with the previous post. We do not know if O is the center and can thus not solve for the area.

Answer: E

Posted from my mobile device

Edited to make that clear.

In that case:

(1) Tells us the diameter of the circle and thus allows us to calculate a range of measurements of the circle. Area is one of those measurements.
However, we have got no information about the shaded area and are thus unable to answer the question.

Not sufficient.

(2) Due to the fact that the lines inside the circles cut through the diameter we will have two pairs of angles of equal measurement. The angles will add up to 360 degrees. In this case we can calculate the portion of the circle that is shaded. But we do not know how large the circle is.

Not sufficient.

(1)+(2) As we know the area of the circle from (1) and the part/whole-relationship between the shaded area and the circle from (2) we can answer the question.

Answer: C

edit:
Another question about assumptions:
Can we assume that we are dealing with only two lines in this question? Couldn't O connect to 4 lines that do not extend each other?

In the figure above, if O is the center of the circle, what is the area of the shaded region?

(1) AB = 8
(2) Angle AOR = 45°.

In order to solve this question we need to know radius length, or diameter (in which case the radius length can be derived) and we also need to know what the angle of either AOP or SOB is.

Statement (1) gives us the length of the diameter because A and B are vertexes on the circumference of the circle; therefore, we know that the radius is 8. However, we do not know the angle of either AOP or SOB- we need either angle in order to calculate the are of the shaded region because those angles are central angles ( graphically assumed). Insufficient.

Statement (2) gives us the angle of AOR which is the opposite the angle of SOB. We can plug 45 as value for X into the area of an arc formula in order to start calculating the area of both arcs; yet, we do not know the radius length. Insufficient.

Each statement, however, provides the other's missing variable- hence, we can combine statement (1) and statement (2) in order to solve the problem.

angle AOR = angle BOS
area of the shaded region =2*angle at the center/360 x pi x r^2

St 1: BA = 2r = 8. therefore r = 4. No idea about the angle. INSUFFICIENT

St 2: angle = 45. No idea about the r. INSUFFICIENT

St 1 & St 2: angle =45 and r=4. putting these value in the above expression, the area can be calculated.

option C