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 177 times ]
2) It can be a Square.

Attachment:

Square.jpg [ 17.65 KiB | Viewed 177 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 quadrilateralAttachment:

Equidiagonal Quandrilateral.jpg [ 36.68 KiB | Viewed 176 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

Answer: C.

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.

Answer C[/quote]

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