Question

Please answer to receive ten points. I'll vote who answers first the brainliest if its correct. 

Answer 1

The distance between points $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$ can be calculated using formula

$P_1P_2=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.$

1.

$AB=\sqrt{(-7-(-11))^2+(8-4)^2}=\sqrt{16+16}=\sqrt{32}=4\sqrt{2}\approx 5.657.$

2.

$AC=\sqrt{(-4-(-11))^2+(4-4)^2}=\sqrt{49+0}=\sqrt{49}=7.$

3.

$CB=\sqrt{(-7-(-4))^2+(8-4)^2}=\sqrt{9+16}=\sqrt{25}=5.$

Then

$P_{ABC}=5.657+7+5=17.657\approx 17.7$

Answer: correct choice is C.