Đáp án:
\[{S_{ABC}} = 7\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
A\left( {0;1} \right);\,\,\,B\left( {2;0} \right);\,\,\,C\left( { - 2; - 5} \right)\\
\Rightarrow \left\{ \begin{array}{l}
\overrightarrow {AB} = \left( {2; - 1} \right)\\
\overrightarrow {BC} = \left( { - 4; - 5} \right)\\
\overrightarrow {CA} = \left( {2;6} \right)
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
AB = \sqrt {{2^2} + {{\left( { - 1} \right)}^2}} = \sqrt 5 \\
BC = \sqrt {{{\left( { - 4} \right)}^2} + {{\left( { - 5} \right)}^2}} = \sqrt {41} \\
CA = \sqrt {{2^2} + {6^2}} = 2\sqrt {10}
\end{array} \right.\\
p = \frac{{AB + BC + CA}}{2} = \frac{{\sqrt 5 + \sqrt {41} + 2\sqrt {10} }}{2}\\
{S_{ABC}} = \sqrt {p\left( {p - AB} \right)\left( {p - BC} \right)\left( {p - CA} \right)} = 7
\end{array}\)
Vậy \({S_{ABC}} = 7\)
