Površina trougla, ako date koordinate njegovih temena \( A\left( x_{1},y_{1} \right),~~B\left( x_{2},y_{2} \right)~~C\left( x_{3},y_{3} \right) \) može se izračunati primenom obrasca
\[ P=\frac{1}{2}\left|x_{1}\left(y_{2}-y_{3} \right) +x_{2}\left(y_{3}-y_{1} \right)+x_{3}\left(y_{1}-y_{2} \right) \right| \].
Primer 1:Izračunati površinu trougla čija su temena tačke А (-2,1), B(3,-1), C(5,-1).
\( P=\frac{1}{2}\left|x_{1}\left(y_{2}-y_{3} \right) +x_{2}\left(y_{3}-y_{1} \right)+x_{3}\left(y_{1}-y_{2} \right) \right| \)
\( P=\frac{1}{2}\left|-2\left(-1+1 \right) +3\left(-1-1 \right)+5\left(1+1 \right) \right| \)
\( P=\frac{1}{2}\left|-2·0 +3·\left( -2\right) +5\left(2 \right) \right| \)
\( P=\frac{1}{2}\left|0 -6+10 \right| \)
\( P=\frac{1}{2}\left|4 \right|=2 \)