The distance between points [tex]P_1(x_1,y_1)[/tex] and [tex]P_2(x_2,y_2)[/tex] can be calculated using formula
[tex]P_1P_2=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.[/tex]
1.
[tex]AB=\sqrt{(-7-(-11))^2+(8-4)^2}=\sqrt{16+16}=\sqrt{32}=4\sqrt{2}\approx 5.657.[/tex]
2.
[tex]AC=\sqrt{(-4-(-11))^2+(4-4)^2}=\sqrt{49+0}=\sqrt{49}=7.[/tex]
3.
[tex]CB=\sqrt{(-7-(-4))^2+(8-4)^2}=\sqrt{9+16}=\sqrt{25}=5.[/tex]
Then
[tex]P_{ABC}=5.657+7+5=17.657\approx 17.7[/tex]
Answer: correct choice is C.
