Edges of triangle is given by equations $\displaystyle a_ix+b_iy+c_i=0\ (i=1,2,3)$.
Prove that the area $\displaystyle P$ of triangle is given with
$\displaystyle
P=\frac{{\Delta}^2}{2|{\Delta}_1{\Delta}_2{\Delta} _3|}$ where $\displaystyle \Delta=\vmatrix
a_1&b_1&c_1\\
a_2&b_2&c_2\\
a_3&b_3&c_3
\endvmatrix ,
$

and $\displaystyle \Delta_i$ are algebric complements of elements $\displaystyle c_i$