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# What is the area of quadrilateral ABCD?

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24 Nov 2012, 09:14
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What is the area of quadrilateral ABCD?

(1) AB = CD = 3
(2) AD = BC = 4
[Reveal] Spoiler: OA
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24 Nov 2012, 12:19
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joylive wrote:
What is the area of quadrilateral ABCD?
(1) AB = CD = 3
(2) AD = BC = 4

1 & 2 together. We still do not know whether given quadrilateral is a rectangle or parallelogram. Insufficient.

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20 Dec 2013, 14:22
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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.
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21 Dec 2013, 06:01
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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.
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02 Apr 2014, 08:17
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OK let's see

First statement we have that the measure of two sides but still no info about the angles. Say we have the quadrilateral ABCD with two adjacent sides measuring 3, meaning all sides are equal to 3. The area could be that of a rhombus or a square. Since we don't know the angles then insufficient

Second statement we have that the measure of two opposite angles is 4. Now, this figure could be anything even an isosceles trapezoid so insufficient

Both statements together we have the measures of the four sides but still without the angles (or slopes if you will) areas will not be fixed.

Therefore E

Hope its clear
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27 Jun 2016, 10:50
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15 Mar 2017, 20:13
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.
What is the area of quadrilateral ABCD?   [#permalink] 15 Mar 2017, 20:13
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