To find the perimeter of a quadrilateral, we need to add the lengths of the sides. For this, we use the distance formula:
[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]Let's solve for each of the sides.
[tex]\begin{gathered} CD=\sqrt{(-2-2)^2+(1-4)^2} \\ \\ CD=\sqrt{16+9} \\ \\ CD=\sqrt{25}=5 \end{gathered}[/tex][tex]\begin{gathered} DE=\sqrt{(2-5)^2+(4-0)^2} \\ DE=\sqrt{9+16} \\ DE=\sqrt{25}=5 \end{gathered}[/tex][tex]\begin{gathered} EF=\sqrt{(5-1)^2+(0-(-3))^2} \\ EF=\sqrt{16+9} \\ EF=\sqrt{25}=5 \end{gathered}[/tex][tex]\begin{gathered} FC=\sqrt{(1-(-2))^2+(-3-1)^2} \\ FC=\sqrt{9+16} \\ FC=\sqrt{25}=5 \end{gathered}[/tex]So each of the sides of the quadrilateral measures 5 units.
The perimiter is the sum of all the sides. P =5 + 5 + 5 + 5 = 4 x 5 = 20 units.
