What is the area of the regular pentagon with a radius of 18mm?

Question

asked Sep 15, 2023 132k views

1 Answer

Rich Scriven · Answer 1 · 2023-09-19T23:26:33+0000

Given:

Required:

We need to find the area of given pantagon

Step-by-step explanation:

First take one triangle with center angle is

$(360)/(5)=72\degree$

now triangle is as

use sin function to find b

$\begin{gathered} sin36=(b)/(r) \\ \\ b=10.58\text{ mm} \end{gathered}$

B is

$B=2b=2*10.58=21.16\text{ mm}$

now to find h

use cos function

$\begin{gathered} cos36=(h)/(r) \\ \\ h=14.56\text{ mm} \end{gathered}$

area of one triangle is

$a=(1)/(2)Bh=(1)/(2)*14.56*21.16=154.07\text{ mm}^2$

area A of pentagone is

Final answer:

$A=5a=770.35\approx770\text{ mm}^2$