Answer :
PERIMETER:
You can calculate the perimeter of a triangle knowing the coordinates, by calculating the distance between every point, as follows:
[tex]\bar{KL}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where x1=-4, y1=-1, x2=-2 and y2=2, replace these values:
[tex]\begin{gathered} \bar{KL}=\sqrt[]{((-2)-(-4))^2+(2-(-1))^2} \\ \bar{KL}=\sqrt[]{(2)^2+(3)^2} \\ \bar{KL}=\sqrt[]{4+9}=\sqrt[]{13}=3.61 \end{gathered}[/tex]Now, you have to do the same for the other segments, let's continue with LM:
[tex]\begin{gathered} \bar{LM}=\sqrt[]{(x_3-x_2)^2+(y_3-y_2)^2} \\ x_3=3\text{ and }y_3=-1\text{ by replacing:} \\ \bar{LM}=\sqrt[]{(3_{}-(-2))^2+((-1)-2)^2} \\ \bar{LM}=\sqrt[]{(5)^2+(-3)^2} \\ \bar{LM}=\sqrt[]{25+9}=\sqrt[]{34}=5.83 \end{gathered}[/tex]Same for segment KM:
[tex]\begin{gathered} \bar{KM}=\sqrt[]{(x_3-x_1)^2+(y_3-y_1)^2} \\ \bar{KM}=\sqrt[]{(3-(-4))^2+((-1)-(-1))^2} \\ \bar{KM}=\sqrt[]{(7)^2+(0)^2} \\ \bar{KM}=\sqrt[]{49+0^{}}=\sqrt[]{49}=7 \end{gathered}[/tex]The perimeter can be calculated as KL+LM+KM:
[tex]\begin{gathered} P=\bar{KL}+\bar{LM}+\bar{KM}=3.61+5.83+7 \\ P=16.44 \end{gathered}[/tex]AREA:
The area can be calculated by using the next formula:
[tex]A=\frac{1}{2}\mleft\lbrace\lbrack(x_1\cdot y_2)+(x_2\cdot y_3)+(x_3\cdot y_1)\mright]-\lbrack(x_1\cdot y_3)+(x_3\cdot y_2)+(x_2\cdot y_1)\rbrack\}[/tex]Then, you have to replace the values to find the area:
[tex]\begin{gathered} A=\frac{1}{2}\lbrace\lbrack((-4)_{}\cdot2)+((-2)\cdot(-1))+(3\cdot(-1))\rbrack-\lbrack((-4)\cdot(-1))+(3\cdot2)+((-2)\cdot(-1))\rbrack\} \\ A=\frac{1}{2}\lbrace\lbrack(-8)+(2)+(-3)\rbrack-\lbrack(4)+(6)+(2)\rbrack\} \\ A=\frac{1}{2}\lbrace\lbrack-9\rbrack-\lbrack12\rbrack\} \\ A=\frac{1}{2}\mleft\lbrace\lvert-21\rvert\mright\rbrace \\ A=\frac{21}{2}=10.50 \end{gathered}[/tex]