Question

find the length of side and the perimeter of a regular nine sided polygon with radius 5units​

Answer 1

Answer:

How do you find the length of a side and the perimeter of a regular nine sided polygon with radius 5 units?

I assume you mean by radius the distance between the centre of the polygon and each of the vertices, not the distance between the centre and the midpoint of each side.

Then you know that each segment is an isosceles triangle with of its sides having length 5 and the angle of the top vertex of 40 degrees. Both base angles are (180–40)/2=70 degrees.

Using the rule of sines, you can now compute the length of the base, which is the side of the nine-sided polygon:

basesin(40)=5sin(70)

I’ll leave the rest of the math to you.

The perimeter would be simply nine times the length of a side.