Answer:
185.1 square units
Step-by-step explanation:
The radius of a regular polygon is the distance from the center to any vertex. Therefore, the radius of the given regular nine-sided polygon is 8 units.
To find the area of a regular polygon given its radius, we can use the following formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Area of a regular polygon}}\\\\A=\dfrac{r^2n\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$n$ is the number of sides.}\\ \phantom{ww}\bullet\;\textsf{$r$ is the radius.}\end{array}}[/tex]
In this case:
Substitute the values into the formula and solve for A:
[tex]A=\dfrac{8^2(9)\sin\left(\dfrac{360^{\circ}}{9}\right)}{2}\\\\\\\\A=\dfrac{64(9)\sin\left(40^{\circ}\right)}{2}\\\\\\\\A=\dfrac{576\sin\left(40^{\circ}\right)}{2}\\\\\\\\A=288\sin(40^{\circ})\\\\\\A=185.1228315897...\\\\\\A=185.1\; \sf square\;units\;(nearest\;tenth)[/tex]
Therefore, the area of the given nonagon rounded to the nearest tenth is:
[tex]\Large\boxed{\boxed{185.1\; \sf square\;units}}[/tex]
