Question

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

Answer 1

The circumradius of the polygon is given below as

`R=17`

Concept:

The perimeter of the nonagon will be calculated using the formula below

`\begin{gathered} P=9* s \\ \text{Where,} \\ s=\text{length of the side} \end{gathered}`

The Length of a side can be calculated using the formula below

`\begin{gathered} s=R*2\sin ((180)/(n)) \\ \text{where,} \\ n=9 \end{gathered}`

By substituting the values, we will have

`\begin{gathered} s=R*2\sin ((180)/(n)) \\ s=17*2\sin ((180)/(9)) \\ s=34\sin 20 \\ \end{gathered}`

Hence,

Substitute the value of s=34sin20 to get the perimeter in the formula below

`\begin{gathered} P=9* s \\ P=9*34\sin 20 \\ P=104.658 \\ P\approx\text{nearest tenth} \\ P=104.7 \end{gathered}`

Hence,

The final answer is P =104.7 units