[tex]AB=\sqrt{(16+8)^2+(16-20)^2}=\sqrt{576+16} =\sqrt{592} =4\sqrt{37} \\\\AC=\sqrt{(12+8)^2+(-8-20)^2} =\sqrt{400+784}= 4\sqrt{74} \\\\BC=\sqrt{(12-16)^2+(-8-16)^2}=4\sqrt{37}[/tex]
Observam ca daca le ridicam la patrat pe fiecare in parte obtinem:
AB²=592
BC²=592
AC²=1184
AC²=AB²+BC²⇒ ΔABC dreptunghic in B, ipotenuza fiind AC
Deci
[tex]A_{ABC}=\frac{AB\times BC}{2} =\frac{4\sqrt{37}\times 4\sqrt{37} }{2} =8\times 37=296cm^2\\\\P_{ABC}=4\sqrt{37}+4\sqrt{37}+4\sqrt{74} =8\sqrt{37}+4\sqrt{74}=4\sqrt{37}(2+\sqrt{2} )cm[/tex]
