Q. 175.0( 3 Votes )
Show that area of the parallelogram whose diagonals are given by and is Also find the area of the parallelogram whose diagonals are
Let ABCD be a parallelogram.
And since, AD ∥ BC
We need to show that,
Where, and are diagonals of the parallelogram ABCD.
Now, by triangle law of addition, we get
Adding equations (i) and (ii), we get
Now, can be written as,
[∵ and ]
We know that,
Vector area of parallelogram ABCD is given by,
Area of parallelogram ABCD
Now, we need to find the area of parallelogram whose diagonals are and .
We have already derived the relationship between area of parallelogram and diagonals of parallelogram, which is
⇒Area of parallelogram
Thus, area of required parallelogram is .
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