PERIMETER:
You can calculate the perimeter of a triangle knowing the coordinates, by calculating the distance between every point, as follows:
![\bar{KL}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}](https://img.qammunity.org/2023/formulas/mathematics/college/ghg5n8gvkd20sclgvshxns31ro84rwczpu.png)
Where x1=-4, y1=-1, x2=-2 and y2=2, replace these values:
![\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}](https://img.qammunity.org/2023/formulas/mathematics/college/eygm5o12ynfftl54wttdnqiojywv9l474n.png)
Now, you have to do the same for the other segments, let's continue with LM:
![\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}](https://img.qammunity.org/2023/formulas/mathematics/college/60ozaxwlf6isft5bnspc516yftrrncglxe.png)
Same for segment KM:
![\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}](https://img.qammunity.org/2023/formulas/mathematics/college/z4im1idoo4yidc9ba4lo9vqmyf54hsaywu.png)
The perimeter can be calculated as KL+LM+KM:

AREA:
The area can be calculated by using the next formula:
![A=(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\}](https://img.qammunity.org/2023/formulas/mathematics/college/tjkuipjm7sohb2ocxvg0bm51th6ruosfj6.png)
Then, you have to replace the values to find the area:
