Given
Perimeter = 30
Find
Area of pentagon
Explanation
as we know area of pentagon =
[tex]area=\frac{1}{2}\times p\times a[/tex]
where a is apothem
Side of pentagon =
[tex]\begin{gathered} \frac{30}{5} \\ 6 \end{gathered}[/tex]
So, to find apothem we apply trignometric ratio
[tex]\begin{gathered} \tan36\degree=\frac{3}{a} \\ a=\frac{3}{\tan36\degree} \\ a=4.13 \end{gathered}[/tex]
area =
[tex]\begin{gathered} \frac{1}{2}\times30\times4.13 \\ 61.95 \end{gathered}[/tex]
Final Answer
The area = 61.95 sq. mi
