Question

O is the center of the regular pentagon below. Find its perimeter. Round to the nearest tenth if necessary.

Answer 1

Answer:

To find the perimeter of the regular pentagon.

O is the center of the regular pentagon from the figure.

we know that, There are 360 degrees around a point, the angle formed over each side are equal that is eual to 360/5 =72

In the triangle made by the side and line joinging center, we get

$72+x+x=180$

whereb x is the angle made by the line joining to the center and one of the side.we get,

$\begin{gathered} 72+2x=180 \\ 2x=108 \end{gathered}$$x=54$

Consider the right angled triangle,

we know that,

$\tan \theta=\frac{opposite\text{ side}}{Adjacent\text{ side}}$

we get,

$\tan 54\degree=\frac{10}{y}$$1.376=\frac{10}{y}$$y=\frac{10}{1.376}$$y=7.26$

Side of a pentagon (s)= 2x7.26=14.52

Perimeter of a pentagon is,

$=5s$$=5\times14.52$$=72.6$

Perimeter of a pentagon is 72.6 units.