What is the area of parallelogram ABCD ?

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

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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Re: Gmat club Please explain [#permalink]

04 Oct 2009, 09:30

tkarthi4u wrote:

What is the area of parallelogram ABCD ?
1) AB = BC = CD = DA = 1
2) AC = BD = (2^1/2)

[Reveal] Spoiler:

(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

Answer: C.
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Re: Gmat club Please explain [#permalink]

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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Re: Gmat club Please explain [#permalink]

05 Oct 2009, 04:29

Thank you. I get it now

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Re: Gmat club Please explain [#permalink]

17 Oct 2009, 15:38

Btw, can anyone tell if there is a comprehensive list of geometric formulas in this forum?

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Re: Gmat club Please explain [#permalink]

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:

Bunuel,
A rhombus and a square with same lengths have different areas?
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Re: Gmat club Please explain [#permalink]

22 Feb 2013, 01:02

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:

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]

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]

22 Feb 2013, 02:06

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]

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]

22 Feb 2013, 02:23

This post received
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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.

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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Re: What is the area of parallelogram ABCD ? 1) AB = BC = CD = [#permalink] 22 Feb 2013, 02:23

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