The corners $(x_1,y_1)$ and $(x_2,y_2)$ and $(x_3,y_3)$ of a triangle.
If $(x_3,y_3)=(0,0)$
The area of the triangle $=\frac{1}{2}\left|\begin{array}{cc}{x}_1& y_1\\ x_2& y_2\end{array}\right|$
otherwise, area $=\frac{1}{2}\left|\begin{array}{ccc}{x}_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1\end{array}\right|$

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the area of the parallelogram:

$\left|\begin{array}{cc}{x}_1& y_1\\ x_2& y_2\end{array}\right|$

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