Cho Delta ABC với A(- 1; - 1)

* Hướng dẫn giải

Phương pháp giải:

Sử dụng công thức: \({S_{ABC}} = \sqrt {p\left( {p - AB} \right)\left( {p - AC} \right)\left( {p - BC} \right)} ,{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} p = \frac{{AB + BC + CA}}{2}.\)

Giải chi tiết:

Ta có: $\{\begin{array}{c}\overrightarrow{AB}=(3;-3)\{\overrightarrow{AC}\mathrm{ }=(5;4)\{\overrightarrow{BC}\mathrm{ }=(2;7)\end{array}\Rightarrow \{\begin{array}{c}AB=3\sqrt{2}\\ AC=\sqrt{41}\\ BC=\sqrt{53}\end{array}\Rightarrow p=\frac{AB+AC+BC}{2}=\frac{3\sqrt{2}\mathrm{ }+\sqrt{41}\mathrm{ }+\sqrt{53}}{2}.$

\( \Rightarrow {S_{ABC}} = \sqrt {p\left( {p - AB} \right)\left( {p - AC} \right)\left( {p - BC} \right)} \)

$=\sqrt{\frac{3\sqrt{2}\mathrm{ }+\sqrt{41}\mathrm{ }+\sqrt{53}}{2}.\frac{\sqrt{41}\mathrm{ }+\sqrt{53}\mathrm{ }-3\sqrt{2}}{2}.\frac{3\sqrt{2}\mathrm{ }+\sqrt{41}-\sqrt{53}}{2}.\frac{3\sqrt{2}\mathrm{ }+\sqrt{53}\mathrm{ }-\sqrt{41}}{2}}$

$=\sqrt{\frac{2916}{16}}\mathrm{ }=\sqrt{\frac{729}{4}}\mathrm{ }=\frac{27}{2}.$