# how to find the area of rhombus if there is only 3 coordinate of the rhombus is given?

This is the question:

Find the area of the rhombus $PQRS$ if the coordinates of point $P$, $Q$ and $R$ are $(6, 4)$, $(8, 7)$ & $(-6, 3)$ respectively.

Does any one know how to solve this?

Thanks!!

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I don't think this is a rhombus - which has all 4 sides equal length... – Juan S Jun 6 '11 at 6:52
Compare math.stackexchange.com/q/424165/139123 -- if you knew all 4 vertices, a good first step in finding the area would be to forget one of them. So if you know only 3 vertices then you are already a step ahead. – David K Jul 1 '15 at 17:27

As that link shows, taking the magnitude of the cross product of two vectors also gives you the area of the parallelogram defined by those two vectors as the non-parallel sides. In your example, $Q$ is an end point of both vectors and as such we can find the vectors
$\vec{QP} = \langle 2,3 \rangle$
$\vec{QR}=\langle 14,4 \rangle$
$||\displaystyle \vec{QP} \times \vec{QR}|| = |2*4 - 14*4| = 48$