Question

This is a regular pentagon. The apothem is shown. What is perimeter of the pentagon? 5 cm OA. 36.3 cm OB. 18.2 cm OC. 43.8 cm OD. 30.7 cm

Answer 1

Given the apothem, we can calculated the length of the side as:

$a=\frac{s}{2\tan (\frac{180}{5})}$

Where:

s = Length of the side

a = Apothem

Solve for s:

$\begin{gathered} s=2a\tan (36) \\ s=2(5)\tan (36) \\ s=7.2654 \end{gathered}$

Therefore, the perimeter is:

$\begin{gathered} P=5\cdot s \\ P=5\cdot(7.2654) \\ P=36.3\operatorname{cm} \end{gathered}$

Answer:

36.3 cm