Notice that we have the following measures for some sides of the figure:
Now, notice the right triangle that we get from the line that passes through A and B, it has sides 2 and 4,then we can find the missing side using the pythagorean theorem:
[tex]\begin{gathered} c^2=(4)^2+(2)^2=16+4=20 \\ \Rightarrow c=\sqrt[]{20}=\sqrt[]{4\cdot5}=2\cdot\sqrt[]{5} \\ c=2\sqrt[]{5} \end{gathered}[/tex]
now that we have that c = 2*sqrt(5), we can find the perimeter:
[tex]\begin{gathered} P=2+2+2+2+2\sqrt[]{5}+2\sqrt[]{5} \\ \Rightarrow P=8+4\sqrt[]{5}=16.9 \\ P=16.9 \end{gathered}[/tex]
therefore, the perimeter of the figure is P = 16.9
