Solution:
The circumradius of the polygon is given below as
[tex]R=17[/tex]
Concept:
The perimeter of the nonagon will be calculated using the formula below
[tex]\begin{gathered} P=9\times s \\ \text{Where,} \\ s=\text{length of the side} \end{gathered}[/tex]
The Length of a side can be calculated using the formula below
[tex]\begin{gathered} s=R\times2\sin (\frac{180}{n}) \\ \text{where,} \\ n=9 \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} s=R\times2\sin (\frac{180}{n}) \\ s=17\times2\sin (\frac{180}{9}) \\ s=34\sin 20 \\ \end{gathered}[/tex]
Hence,
Substitute the value of s=34sin20 to get the perimeter in the formula below
[tex]\begin{gathered} P=9\times s \\ P=9\times34\sin 20 \\ P=104.658 \\ P\approx\text{nearest tenth} \\ P=104.7 \end{gathered}[/tex]
Hence,
The final answer is P =104.7 units
