Question

What is the area of the figure? Show your work to find the side of the length, apothem, and the area using 1/2Pa.

Answer 1

Given

Perimeter = 30

Find

Area of pentagon

Step-by-step explanation

as we know area of pentagon =

`area=(1)/(2)* p* a`

where a is apothem

Side of pentagon =

`\begin{gathered} (30)/(5) \\ 6 \end{gathered}`

So, to find apothem we apply trignometric ratio

`\begin{gathered} \tan36\degree=(3)/(a) \\ a=(3)/(\tan36\degree) \\ a=4.13 \end{gathered}`

area =

`\begin{gathered} (1)/(2)*30*4.13 \\ 61.95 \end{gathered}`

Final Answer

The area = 61.95 sq. mi