Question

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

Answer 1

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=(10)/(y)`
`1.376=(10)/(y)`
`y=(10)/(1.376)`
`y=7.26`

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

Perimeter of a pentagon is,

`=5s`
`=5*14.52`
`=72.6`

Perimeter of a pentagon is 72.6 units.