Bunuel wrote:

bluecatie1 wrote:

What is the area of quadrilateral ABCD?

(1) AB = CD = 3

(2) AD = BC = 4

Statement 2 tells us that the diagonals are equal which is only applicable to either squares or rectangles, because all four of the above mentioned quadrilaterals have all angles equal to 90 degrees. If the quadrilateral were a square, then the diagonal would be equal to root3. Since the diagonal is equal to 4 then it must be a rectangle. I vote for C.

Notice that AD and BC are NOT diagonals, they are sides of the quadrilateral. The correct answer is E.

I think it's important to note that when we don't have a diagram of a figure, such as ABCD, the order of the points moves in a clock wise fashion. For example in Square ABCD, the top left point is A, the top right point is B, the bottom right point is C, and the bottom left point is D. I learned this order just by looking at figures in prep books and on Gmatclub.

Anyways, this question asks us to find the area of quadrilateral ABCD- first, we must know what type of quadrilateral we're dealing with because different quadrilaterals have different formulas for their areas.

Statement (1) tells us that AB and CD, which are parallel sides, are equal. However, we can have two parallel sides in a parallelogram or rectangle. Insufficient.

Statement (2) tells us that AD and BC, which are also parallel sides, are equal. However, this piece of information also leaves us with the same problem- we don't know if this figure is a parallelogram or rectangle. Insufficient.

Statement (1) and Statement (2) combined state that all sides of the figure are congruent. Though, again, this figure could be a parallelogram or rectangle. Insufficient.

Therefore, neither Statement (1) nor Statement (2) is sufficient.