Apothem and radius problems

[SomeoneYouDontKnow]

So I have 4 questions about this.
1. I need to find the function for the perimeter of a regular polygon given the number of sides, and the length of the apothem

2. I need to find the function for the area of a regular polygon given the number of sides, and the length of the apothem

3. I need to find the function for the perimeter of a regular polygon given the number of sides, and the length of the radius

4.I need to find the function for the area of a regular polygon given the number of sides, and the length of the radius

 

[nasi112]

Your question is related to something I just did. You can follow my work through this link.

Perimeter of Regular Polygon

Find the perimeter of a regular polygon of 180 sides inscribed in a circle of diameter 1.00000 m. Compare this number with the circumference of the circle. I try to solve this question geometrically. I can't draw 180 sides, so I drew a few. I found this. I need software name that can draw...

www.freemathhelp.com

 

[fresh_42]

The trick to investigating the triangle built from two neighboring points of the polygon and the center of the circle surrounding it.

 

[mrtwhs]

So I have 4 questions about this.
1. I need to find the function for the perimeter of a regular polygon given the number of sides, and the length of the apothem

2. I need to find the function for the area of a regular polygon given the number of sides, and the length of the apothem

3. I need to find the function for the perimeter of a regular polygon given the number of sides, and the length of the radius

4.I need to find the function for the area of a regular polygon given the number of sides, and the length of the radius

What are the restrictions on the formulas? Some of these are basic high school geometry. Others will need trigonometry.

 

[Dr.Peterson]

Your question is related to something I just did. You can follow my work through this link.

Perimeter of Regular Polygon

Find the perimeter of a regular polygon of 180 sides inscribed in a circle of diameter 1.00000 m. Compare this number with the circumference of the circle. I try to solve this question geometrically. I can't draw 180 sides, so I drew a few. I found this. I need software name that can draw...

www.freemathhelp.com

Why do you respond to a 10 year old problem? They aren't still waiting.

 

[MarkOlwen]

So I have 4 questions about this.
1. I need to find the function for the perimeter of a regular polygon given the number of sides, and the length of the apothem

2. I need to find the function for the area of a regular polygon given the number of sides, and the length of the apothem

3. I need to find the function for the perimeter of a regular polygon given the number of sides, and the length of the radius

4.I need to find the function for the area of a regular polygon given the number of sides, and the length of the radius

Can you clarify whether you want these formulas expressed purely in terms of n and the apothem/radius, or are you also looking for a geometric explanation of how each formula is derived?

 

[The Highlander]

Can you clarify whether you want these formulas expressed purely in terms of n and the apothem/radius, or are you also looking for a geometric explanation of how each formula is derived?

Please read through all the posts already made in a thread before jumping in with a contribution that may be
somewhat redundant.

In particular, you should have noted what was said in the post immediately preceding yours (qv).

Helpful contributions are always welcome but just wanting to make your presence felt can not only be counter productive but also a waste of space.