# How do you find the area of the parallelogram with vertices: p(0,0,0), q(-5,0,4), r(-5,1,2), s(-10,1,6)?

Mar 23, 2018

$\sqrt{141}$?

#### Explanation:

The area of a parallelogram is the magnitude of the cross-product of any two non-parallel sides.
Take $\vec{P Q}$ and $\vec{P R}$, say, because they share a point and so can't be parallel:
$| | \left(\hat{i} , \hat{j} , \hat{k}\right) , \left(- 5 , 0 , 4\right) , \left(- 5 , 1 , 2\right) | |$
$= \sqrt{16 + 100 + 25}$
=$\sqrt{141}$ (if my vector multiplication and scalar multiplication are correct!)