Find perimeter of a n-gon based on radius and # of sides

[airon]

Example:

The radius is 8, and it has 16 sides (16-gon).

Can someone please give me a formula to solve for the perimeter of this polygon? Preferably it will be explained a little as well.

Thanks,

Airon.

 

[Deleted member 4993]

Example:

The radius is 8, and it has 16 sides (16-gon).

Can someone please give me a formula to solve for the perimeter of this polygon? Preferably it will be explained a little as well.

Thanks,

Airon.

Please show us your work and exactly where you are stuck - so that we know exactly where to begin to help you.

Hint:

Divide the polygon into n-small triangles with the radius as sides and one of the vertices at the center.

 

[airon]

Hi sorry this isn't really for school or anything. Anyways I don't know where to start other than trig (which I haven't learned yet).

If I break it up into individual segements:

You know both radius sides are 8... well because the radius is 8. You also know the included angle is 22.5 degrees because the polygon has 16 sides, so (360 / 16 = 22.5).

If I could find what "x" is, I could multiply that by 16 to find the perimeter, I assume?

Can someone explain how to do this? And if this isn't the most efficient method, is there a simpler way to solve?

Thanks.

 

[Deleted member 4993]

You are correct - uptill now - however as far as I know you need to use trig after this.

x = 2 * R * sin(11.25) and most efficient way would be to use a calculator.

 

[airon]

So basically, you pull out a 2 from the included angle, and find the sin of the new number? Then multiply by the radius and multiply back in the 2?