Given the apothem, we can calculated the length of the side as:
[tex]a=\frac{s}{2\tan (\frac{180}{5})}[/tex]
Where:
s = Length of the side
a = Apothem
Solve for s:
[tex]\begin{gathered} s=2a\tan (36) \\ s=2(5)\tan (36) \\ s=7.2654 \end{gathered}[/tex]
Therefore, the perimeter is:
[tex]\begin{gathered} P=5\cdot s \\ P=5\cdot(7.2654) \\ P=36.3\operatorname{cm} \end{gathered}[/tex]
Answer:
36.3 cm
