Question

set up trigonometric ratios for three separate regular pentagons with different givens:

Answer 1

Solution

From the taingle

Using trigonometric ratio it follow

The length ofa sde of the pentagon is

$\begin{gathered} 2\times5tan36 \\ = \end{gathered}$

Therefore the perimeter of the pentagon is \:

$\begin{gathered} 5\times2\times5\times\tan36 \\ =50tan36 \\ =36.32 \end{gathered}$

Therefore the area of the perimter is

$\begin{gathered} A=\frac{1}{2}\times36.32\times5 \\ A=90.8 \end{gathered}$