The perimeter of the pentagon ABCDE is given by:
[tex]P=AB+BC+CD+DE+EA[/tex]
From the figure, we can calculate the length of each side:
[tex]\begin{gathered} AB=\sqrt{4^2+1^2}=\sqrt{17} \\ \\ BC=\sqrt{1^2+3^2}=\sqrt{10} \\ \\ CD=\sqrt{6^2+3^2}=3\sqrt{5} \\ \\ DE=\sqrt{1^2+3^2}=\sqrt{10} \\ \\ EA=\sqrt{2^2+4^2}=2\sqrt{5} \end{gathered}[/tex]
Finally, the perimeter is:
[tex]\begin{gathered} P=\sqrt{17}+\sqrt{10}+3\sqrt{5}+\sqrt{10}+2\sqrt{5}=\sqrt{17}+2\sqrt{10}+5\sqrt{5} \\ \\ \therefore P\approx21.628 \end{gathered}[/tex]
