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yashikaaggarwal
chetan2u

So, the diagonals are twice of the values given ..
AC=2*4=8 and BD=2*6=12
Sir, Why did you took diagonal value twice of the given data. Its perpendicular bisector is not given. Kindly Explain

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The diagonals bisect each other in a parallelogram so the diagonals will be twice of the values given.
If P is equidistant from the two points at more than one place then that line is perpendicular. Here O and P are equidistant from B and D
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=>

Since diagonals of a parallelogram bisect each other, we have \(OA = OC = 4\) and \(OB = OD = 6.\)

Then triangles \(OBP\) and \(ODP\) are congruent.

Thus, we have \(∠POB = ∠POD = 90°.\)

Since two diagonals of a parallelogram are perpendicular to each other, the parallelogram is a rhombus.
Then the area of the rhombus is \((\frac{1}{2})·8·12 = 48.\)

Therefore, D is the answer.
Answer: D
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