# Nonagon

#### BrendanLoftus

What is the area of a Nonagon if the radius is 8 in. Answer must be rounded to the nearest tenth.

Here is some of my work.
I found a formula online that could help. It was nr^2tan(180/n) where n=number of sides and r=radius

If that is the case, I got 576(tan20) as an answer, which equals 1288.6 rounded......I have doubts to that answer....

Am I right or wrong....Any help is greatly appreciated....

Is there a possible generalization to this too? (for any # sided polygon)

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#### earboth

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What is the area of a Nonagon if the radius is 8 in. Answer must be rounded to the nearest tenth.

Here is some of my work.
I found a formula online that could help. It was nr^2tan(180/n) where n=number of sides and r=radius

If that is the case, I got 576(tan20) as an answer, which equals 1288.6 <<<<<< how did you get this result?
rounded......I have doubts to that answer....

Am I right or wrong....Any help is greatly appreciated....

Is there a possible generalization to this too? (for any # sided polygon)
1. I assume that you mean a regular nonagon ....?

2. You didn't mention if "the radius" belongs to the incircle of the nonagon or the circumscribed circle.

3. The formula you used gives the area of a regular nonagon with an incircle of r = 8.

4. To derive a general formula to calculate the area consider a regular n-gon as n isosceles congruent triangles. You can calculate the base and the height of one triangle using the radius of the circle.

5. Btw $$\displaystyle 576\cdot \tan(20^\circ)\approx 209.65$$

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