In the figure above, if the area of the rectangular region PQRS is 40,

Since we don’t know the length and width of rectangle PSRS (for example, l = 10 and w = 4 OR l = 8 and w = 5), we don’t know the length of PS. Furthermore, since we do not know whether T is the center of the rectangle, there is no way for us to determine the height of triangle PTS, and thus no way to determine the area of the pentagonal region PQRST.

Alternate Explanation:

Figure not drawn to scale means that the point T could be anywhere within the rectangle that satisfies PT = TS; in other words, it could be anywhere on the vertical line that passes through T. If we imagine that point T is located very close to the side PS of the rectangle, the area of the triangle will be very small and the area of the pentagonal region will be close to the area of the rectangle. If, on the other hand, point T is located very close to the side QR of the rectangle, then the area of the triangle will be larger and the area of the pentagonal region will be smaller. Thus, the information provided in the question does not determine the area of the pentagonal region PQRST.

Answer: E