This is true if the base of the rectangle bisects along the diameter; what if it doesn't? Nothing specifies that the base of the rectangle = the diameter.

Scott, the problem says explicitly that it is a "semicircle inscribed in the rectangle", so it pretty much is established that the base of the rectangle is the diameter of the circle.

The explanation says "calculating the percent of the rectangle that is shaded yields....25%." That would make column A ("percent of the rectangle that is shaded") and column B (25%) equal. In that case, the answer doesn't make sense. What am I missing here?

Ok I see that now, thank you.

I do have another question. The solution says that "we can assume the dimensions are independent of the solution." How can we determine when the dimensions (or anything else) should be assumed vs realizing there is not enough information. For example, when it comes to triangles, we should not assume dimensions based on the drawing. I particularly remember a question where one angle of the triangle drawn was clearly larger than 90 and clearly obtuse (as in at least 120 degrees) but the solution told us we can't assume that it is obtuse and not acute. When do we know when to assume and when to not assume?

I can't understand why the solution is B. If we take the radius of the circle to be r, then the shaded area is ((4-pi)r^2)/2, and this can be less, equal or more than 25%. Please show me where the mistake is, if there is any.

Just a note for a bug fix. I have an iPhone and many of your solutions don't show the full answer