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# What is the area of parallelogram ABCD ?

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

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09 Sep 2015, 02:09
earnit wrote:
Bunuel wrote:
tkarthi4u wrote:
What is the area of parallelogram ABCD ?
1) AB = BC = CD = DA = 1
2) AC = BD = (2^1/2)

(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.

_______________
Yes, that's correct.
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Re: What is the area of parallelogram ABCD ?  [#permalink]

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07 Sep 2017, 20:24
tkarthi4u wrote:
What is the area of parallelogram ABCD ?

(1) AB = BC = CD = DA = 1
(2) AC = BD = (2^1/2)

Statement 1

Knowing just the side lengths of a parallelogram does not allow us to find the area. There are two scenarios, the parallelogram could be a rhombus or more specifically a square. If the shape were a square, then we would be able to find the area of ABCD. If the shape is a just a rhombus in general then we cannot find the length of the diagonal of the rhombus.

Statement 2

Knowing the lengths of the diagonals is not sufficient either as ABCD could be a recentagle.

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

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08 Sep 2017, 20:12
Statement A alone is also sufficient: If we go by hero's formula = sq rt*(s-a)(s-b)(s-c)(s-d)... But B alone is not sufficient..

Plz help!!
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Posts: 51227
Re: What is the area of parallelogram ABCD ?  [#permalink]

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08 Sep 2017, 21:13
Ruchita1907 wrote:
Statement A alone is also sufficient: If we go by hero's formula = sq rt*(s-a)(s-b)(s-c)(s-d)... But B alone is not sufficient..

Plz help!!

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

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11 May 2018, 19:29
Hii
if we know one of the diagonal length & we know that it is a rhombus ( as all sides are equal)
We can find the length of both diagonals using geometrical properties and also the area. (Tag me if you want to know the procedure)
Area of rhombus = (product of diagonal/2)

Answer would be C in that case also.

vietnammba wrote:
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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Re: What is the area of parallelogram ABCD ?  [#permalink]

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11 May 2018, 19:36
Hi

the area of rhombus is not fixed only by the length of sides of rhombus.
To find are of rhombus, following information required:
1) Both diagonals
2) sides and angle between sides.
3) sides and a diagonal

In fact Square has the max area of all the rhombus having same side lengths.
Attachment:

WhatsApp Image 2018-05-12 at 08.55.17.jpeg [ 61.09 KiB | Viewed 234 times ]

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?

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

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11 May 2018, 22:53
Hi

There is a serious flaw in your interpretation of Statement 2:

if a Quadrilateral has equal diagonals, nothing unique can be interpreted from it.

1) It can be a Rectangle
Attachment:

Rectangle.jpg [ 9.83 KiB | Viewed 207 times ]

2) It can be a Square.
Attachment:

Square.jpg [ 17.65 KiB | Viewed 207 times ]

3) It can't be rhombus.= It can be a rhombus, ( Square is a particular case of rhombus)
In rhombus the diagonals, need not to be equal, but they can be equal and this case is called Square.

4) it can be any Equidiagonal quadrilateral
Attachment:

Equidiagonal Quandrilateral.jpg [ 36.68 KiB | Viewed 206 times ]

But since It is given in the question that the quadrilateral is a parallelogram, the quadrilateral in the question is not this type of Quadrilateral.
But this is important for the conceptual knowledge.

earnit wrote:
tkarthi4u wrote:
What is the area of parallelogram ABCD ?
1) AB = BC = CD = DA = 1
2) AC = BD = (2^1/2)

(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.

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What is the area of parallelogram ABCD ? &nbs [#permalink] 11 May 2018, 22:53

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