The cross product $\mathrm{dseg1}X\mathrm{dseg2}$ can be interpret as the signed area of the parallelogram formed by the point $0,0$, dseg1, dseg2 and $\mathrm{dseg1}+\mathrm{dseg2}$.

Note that the tails of dseg1 and dseg2 must be the same.

The command with(geometry,CrossProduct) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{point}\left(A\,0\,0\right),\mathrm{point}\left(B\,1\,1\right),\mathrm{point}\left(C\,11\,5\right)\:$

$\mathrm{dsegment}\left(\mathrm{dseg1}\,A\,B\right)\:$$\mathrm{dsegment}\left(\mathrm{dseg2}\,A\,C\right)\:$

$\mathrm{CrossProduct}\left(\mathrm{dseg1}\,\mathrm{dseg2}\right)$

$\mathrm{-6}$

$\mathrm{triangle}\left(T\,\left[A\,B\,C\right]\right)$

$T$

$\mathrm{area}\left(T\right)$

$3$