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- Thread starter suvadip
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- Mar 10, 2012

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Hint: If the diagonals of a parallelogram are known then you can find the sides. Figure out how.I can find the area of the parallelogram when two adjacent side vectors are given. But how to find the area of the parallelogram when diagonals of the parallelogram are given as

\(\displaystyle \alpha = 2i+6j-k\) and \(\displaystyle \beta= 6i-8j+6k\)

- Jan 30, 2012

- 74

Here is a slightly different way to calculate the area of a parallelogram:I can find the area of the parallelogram when two adjacent side vectors are given. But how to find the area of the parallelogram when diagonals of the parallelogram are given as

\(\displaystyle \alpha = 2i+6j-k\) and \(\displaystyle \beta= 6i-8j+6k\)

According to your question \(\displaystyle \alpha\) and \(\displaystyle \beta\) denote the diagonals of a parallelogram. Then the area is

\(\displaystyle A = \frac12 \cdot \| \vec {\alpha} \times \vec {\beta} \|\)