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The area of parallelogram ABCD

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The area of parallelogram ABCD [#permalink] New post 18 Sep 2018, 10:44
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Question Stats:

41% (00:51) correct 58% (00:00) wrong based on 24 sessions
Attachment:
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Quantity A
Quantity B
15
The area of parallelogram
ABCD


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The area of parallelogram ABCD [#permalink] New post 19 Sep 2018, 09:09
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Carcass wrote:
Attachment:
para.jpg




Quantity A
Quantity B
15
The area of parallelogram
ABCD


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Area of parallelogram = (base)(height)
Area of rectangle= (base)(height)


KEY CONCEPT: If ∠BAD were 90°, then quadrilateral BADC would be a rectangle.
As a rectangle, the base would have length 3 and the height would be 5
So, the area WOULD be 15


However, since ∠BAD is actually 65°, the height of the quadrilateral must be LESS THAN 5 (parallelogram BADC is basically a rectangle that has been "pushed over" to be made shorter).
So, area of BADC = (3)(some value that LESS THAN 5)
= some value that's LESS THAN 15

So, we have:
Quantity A: 15
Quantity B: some value that's LESS THAN 15

Answer: A

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Re: The area of parallelogram ABCD   [#permalink] 19 Sep 2018, 09:09
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