Given:
Required:
We need to find the area of given pantagon
Explanation:
First take one triangle with center angle is
[tex]\frac{360}{5}=72\degree[/tex]
now triangle is as
use sin function to find b
[tex]\begin{gathered} sin36=\frac{b}{r} \\ \\ b=10.58\text{ mm} \end{gathered}[/tex]
B is
[tex]B=2b=2*10.58=21.16\text{ mm}[/tex]
now to find h
use cos function
[tex]\begin{gathered} cos36=\frac{h}{r} \\ \\ h=14.56\text{ mm} \end{gathered}[/tex]
area of one triangle is
[tex]a=\frac{1}{2}Bh=\frac{1}{2}*14.56*21.16=154.07\text{ mm}^2[/tex]
area A of pentagone is
Final answer:
[tex]A=5a=770.35\approx770\text{ mm}^2[/tex]
