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

Question

asked Jan 4, 2023 59.5k views

1 Answer

Agabrys · Answer 1 · 2023-01-10T14:40:02+0000

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

$a=(s)/(2\tan ((180)/(5)))$

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