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What is the area of quadrilateral ABCD?

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What is the area of quadrilateral ABCD? [#permalink] New post 24 Nov 2012, 08:14
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A
B
C
D
E

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Question Stats:

50% (02:01) correct 50% (00:29) wrong based on 79 sessions
What is the area of quadrilateral ABCD?

(1) AB = CD = 3
(2) AD = BC = 4
[Reveal] Spoiler: OA
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Re: What is the area of quadrilateral ABCD? [#permalink] New post 24 Nov 2012, 11:19
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joylive wrote:
What is the area of quadrilateral ABCD?
(1) AB = CD = 3
(2) AD = BC = 4


1) No information about AD,BC and slope of AB,CD,AD and BC. Insufficient.

2) No information about AD,BC and slope of AB,CD,AD and BC. Insufficient.

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

Answer should be E.

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Re: What is the area of quadrilateral ABCD? [#permalink] New post 20 Dec 2013, 13:22
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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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Re: What is the area of quadrilateral ABCD? [#permalink] New post 21 Dec 2013, 05:01
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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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Re: What is the area of quadrilateral ABCD? [#permalink] New post 02 Apr 2014, 07:17
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
Cheers
J
Re: What is the area of quadrilateral ABCD?   [#permalink] 02 Apr 2014, 07:17
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