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# What is the area of parallelogram ABCD ?

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What is the area of parallelogram ABCD ? [#permalink]

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04 Oct 2009, 08:30
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What is the area of parallelogram ABCD ?

(1) AB = BC = CD = DA = 1
(2) AC = BD = (2^1/2)
[Reveal] Spoiler: OA
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04 Oct 2009, 09:30
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tkarthi4u wrote:
What is the area of parallelogram ABCD ?
1) AB = BC = CD = DA = 1
2) AC = BD = (2^1/2)

[Reveal] Spoiler:
C

(1) Says that ABCD is a rhombus. Area of rhombus d1*d2/2 (d1 and d2 are the lengths of the diagonals) or b*h (b is the length of the base, h is the altitude (height).) Insufficient

(2) Says that ABCD is a rectangle. Area of a rectangle L*W (length*width) Insufficient.

(1)+(2) ABCD is rectangle and rhombus --> ABCD is square --> Area=1^2=1 or (2^1/2)*(2^1/2)/2=1

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05 Oct 2009, 00:56
"Area of rhombus d1*d2/2 (d1 and d2 are the lengths of a diagonals)"

Didn't know that! Thanks.
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22 Feb 2013, 00:37
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Bunuel wrote:
tkarthi4u wrote:
What is the area of parallelogram ABCD ?
1) AB = BC = CD = DA = 1
2) AC = BD = (2^1/2)

[Reveal] Spoiler:
C

(1) Says that ABCD is a rhombus. Area of rhombus d1*d2/2 (d1 and d2 are the lengths of a diagonals) or b*h (b is the length of the base, h is the altitude (height).) Insufficient

(2) Says that ABCD is a rectangle. Area of a rectangle L*W (length*width) Insufficient.

(1)+(2) ABCD is rectangle and rhombus --> ABCD is square --> Area=1^2=1 or (2^1/2)*(2^1/2)/2=1

C.

Bunuel,
A rhombus and a square with same lengths have different areas?
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22 Feb 2013, 01:02
Expert's post
Sachin9 wrote:
Bunuel wrote:
tkarthi4u wrote:
What is the area of parallelogram ABCD ?
1) AB = BC = CD = DA = 1
2) AC = BD = (2^1/2)

[Reveal] Spoiler:
C

(1) Says that ABCD is a rhombus. Area of rhombus d1*d2/2 (d1 and d2 are the lengths of a diagonals) or b*h (b is the length of the base, h is the altitude (height).) Insufficient

(2) Says that ABCD is a rectangle. Area of a rectangle L*W (length*width) Insufficient.

(1)+(2) ABCD is rectangle and rhombus --> ABCD is square --> Area=1^2=1 or (2^1/2)*(2^1/2)/2=1

C.

Bunuel,
A rhombus and a square with same lengths have different areas?

Good question.

If you squeeze a square along its diagonal you'll get a rhombus. Different rhombuses you'll get while doing that, will have different area. So, the answer to your question is yes.

Hope it's clear.
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Re: What is the area of parallelogram ABCD ? 1) AB = BC = CD = [#permalink]

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22 Feb 2013, 02:01
Pardon me. I didn't get you, Bunuel..

Are you saying that the square and different shapes of rhombuses with same length will have different areas?
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Re: What is the area of parallelogram ABCD ? 1) AB = BC = CD = [#permalink]

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22 Feb 2013, 02:06
Expert's post
Sachin9 wrote:
Pardon me. I didn't get you, Bunuel..

Are you saying that the square and different shapes of rhombuses with same length will have different areas?

Yes, that's what I'm saying.
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Re: What is the area of parallelogram ABCD ? 1) AB = BC = CD = [#permalink]

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22 Feb 2013, 02:12
Bunuel wrote:
Sachin9 wrote:
Pardon me. I didn't get you, Bunuel..

Are you saying that the square and different shapes of rhombuses with same length will have different areas?

Yes, that's what I'm saying.

ok thanks..
Now 2 questions:
1)if the square and different shapes of rhombuses with same length will have different areas, the square will have the largest area . Guess this is correct.

2)this question seems dubious now to me.. A square is also a parallelogram and even a rhombus is.. so how can we be sure that ABCD is not a square and is a rhombus.
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Re: What is the area of parallelogram ABCD ? 1) AB = BC = CD = [#permalink]

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22 Feb 2013, 02:23
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Expert's post
Sachin9 wrote:
Bunuel wrote:
Sachin9 wrote:
Pardon me. I didn't get you, Bunuel..

Are you saying that the square and different shapes of rhombuses with same length will have different areas?

Yes, that's what I'm saying.

ok thanks..
Now 2 questions:
1)if the square and different shapes of rhombuses with same length will have different areas, the square will have the largest area . Guess this is correct.

2)this question seems dubious now to me.. A square is also a parallelogram and even a rhombus is.. so how can we be sure that ABCD is not a square and is a rhombus.

Not sure I understand what you are trying to say.

Anyway:
From (1) we have that the parallelogram is also a rhombus (because the sides are equal).
From (2) we have that the parallelogram is also a rectangle (because the diagonals are equal).

So, our parallelogram is a rhombus AND a rectangle, so it's a square!
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18 Jun 2014, 07:02
Bunuel wrote:
tkarthi4u wrote:
What is the area of parallelogram ABCD ?
1) AB = BC = CD = DA = 1
2) AC = BD = (2^1/2)

[Reveal] Spoiler:
C

(1) Says that ABCD is a rhombus. Area of rhombus d1*d2/2 (d1 and d2 are the lengths of a diagonals) or b*h (b is the length of the base, h is the altitude (height).) Insufficient

(2) Says that ABCD is a rectangle. Area of a rectangle L*W (length*width) Insufficient.

(1)+(2) ABCD is rectangle and rhombus --> ABCD is square --> Area=1^2=1 or (2^1/2)*(2^1/2)/2=1

HI Bunuel,
Square root of 2 is diagonal.

\sqrt{2}, 1,1 form right angle triangle in rectangle. as we follow this rule in GMAT,cant we follow here ,considering length and breadth to be 1 each??
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18 Jun 2014, 08:37
Expert's post
nidhi12 wrote:
Bunuel wrote:
tkarthi4u wrote:
What is the area of parallelogram ABCD ?
1) AB = BC = CD = DA = 1
2) AC = BD = (2^1/2)

[Reveal] Spoiler:
C

(1) Says that ABCD is a rhombus. Area of rhombus d1*d2/2 (d1 and d2 are the lengths of a diagonals) or b*h (b is the length of the base, h is the altitude (height).) Insufficient

(2) Says that ABCD is a rectangle. Area of a rectangle L*W (length*width) Insufficient.

(1)+(2) ABCD is rectangle and rhombus --> ABCD is square --> Area=1^2=1 or (2^1/2)*(2^1/2)/2=1

HI Bunuel,
Square root of 2 is diagonal.

\sqrt{2}, 1,1 form right angle triangle in rectangle. as we follow this rule in GMAT,cant we follow here ,considering length and breadth to be 1 each??

Next, are you talking about the second statement? What does "$$\sqrt{2}$$, 1, 1 form right angle triangle in rectangle" even mean? Or the next sentence in your post? Sorry, don't understand at all what you mean...
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Re: What is the area of parallelogram ABCD ? [#permalink]

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16 Sep 2014, 12:50
Bunuel wrote:
tkarthi4u wrote:
What is the area of parallelogram ABCD ?
1) AB = BC = CD = DA = 1
2) AC = BD = (2^1/2)

[Reveal] Spoiler:
C

(1) Says that ABCD is a rhombus. Area of rhombus d1*d2/2 (d1 and d2 are the lengths of the diagonals) or b*h (b is the length of the base, h is the altitude (height).) Insufficient

(2) Says that ABCD is a rectangle. Area of a rectangle L*W (length*width) Insufficient.

(1)+(2) ABCD is rectangle and rhombus --> ABCD is square --> Area=1^2=1 or (2^1/2)*(2^1/2)/2=1

Bunuel,

Since a square is also parallelogram, we have sides of a sq so easily we can find the area.
Shouldn't A be sufficient?

Regards,
Ravi
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Re: What is the area of parallelogram ABCD ? [#permalink]

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16 Sep 2014, 13:24
Expert's post
email2vm wrote:
Bunuel wrote:
tkarthi4u wrote:
What is the area of parallelogram ABCD ?
1) AB = BC = CD = DA = 1
2) AC = BD = (2^1/2)

[Reveal] Spoiler:
C

(1) Says that ABCD is a rhombus. Area of rhombus d1*d2/2 (d1 and d2 are the lengths of the diagonals) or b*h (b is the length of the base, h is the altitude (height).) Insufficient

(2) Says that ABCD is a rectangle. Area of a rectangle L*W (length*width) Insufficient.

(1)+(2) ABCD is rectangle and rhombus --> ABCD is square --> Area=1^2=1 or (2^1/2)*(2^1/2)/2=1

Bunuel,

Since a square is also parallelogram, we have sides of a sq so easily we can find the area.
Shouldn't A be sufficient?

Regards,
Ravi

For (1) we have a parallelogram with equal sides, so rhombus, not necessarily a square.
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Re: What is the area of parallelogram ABCD ? [#permalink]

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23 Nov 2014, 05:55
Bunuel, how can we be sure in such questions that AB or BC is a side? I encountered several such questions in gmatclub tests and if I remember correctly, there was a question which consisted of such trick.
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Re: What is the area of parallelogram ABCD ? [#permalink]

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23 Nov 2014, 06:58
Expert's post
Ergenekon wrote:
Bunuel, how can we be sure in such questions that AB or BC is a side? I encountered several such questions in gmatclub tests and if I remember correctly, there was a question which consisted of such trick.

We are given that ABCD is a parallelogram (we should trust the order of letters on the GMAT). So AB, BC, CD and DA must be its sides. How else? Can you please given me the links to the questions you are talking about.
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Re: What is the area of parallelogram ABCD ? [#permalink]

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23 Nov 2014, 07:21
Ok. Thanks Bunuel. I do not have the links now, but when I encounter such things again I will post it here.
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Re: What is the area of parallelogram ABCD ? [#permalink]

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02 Dec 2014, 02:42
Hi Bunuel,

If the second statement states that the diagonal length is different from square root of 2, the right choice will be E?
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What is the area of parallelogram ABCD ? [#permalink]

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27 Jan 2015, 06:35
Dear Bunuel, I want to ask you about the second statment AC=BD=2^1/2.You said that this could be rectangular how

we can get diagonals of rectangular with lengths equal to 2^1/2? Where the sides of rectangular are not equal. So, I

think that we can get diagonals equals to 2^1/2 just if we have both sides are equals to 1. Therefore, I see that the

form can not be rectangular. Please correct me if what I wrote is not right.

Also, I want to ask you about the diagonals of rhombus do they should be equals? and how we can calculate diagonals

of rhombus I mean which form we can use?

Thank you
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Re: What is the area of parallelogram ABCD ? [#permalink]

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19 Feb 2015, 01:52
What if the length of diagonal in statement B was not 2^1/2?
Would the answer still be C?
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Re: What is the area of parallelogram ABCD ? [#permalink]

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09 Sep 2015, 01:08
Bunuel wrote:
tkarthi4u wrote:
What is the area of parallelogram ABCD ?
1) AB = BC = CD = DA = 1
2) AC = BD = (2^1/2)

[Reveal] Spoiler:
C

(1) Says that ABCD is a rhombus. Area of rhombus d1*d2/2 (d1 and d2 are the lengths of the diagonals) or b*h (b is the length of the base, h is the altitude (height).) Insufficient

(2) Says that ABCD is a rectangle. Area of a rectangle L*W (length*width) Insufficient.

(1)+(2) ABCD is rectangle and rhombus --> ABCD is square --> Area=1^2=1 or (2^1/2)*(2^1/2)/2=1

I would really appreciate if a fault in my logic is pointed out.

Statement 1: ABCD is either a square or a rhombus, so different areas. Insufficient.

Statement 2: ABCD is a parallelogram with equal diagonals, so cannot be a rhombus. Possibly a rectangle or a square. Insufficient.

1+2. It must be a square.

Re: What is the area of parallelogram ABCD ?   [#permalink] 09 Sep 2015, 01:08

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