## Area of triangle

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

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