# Math question: How to compute the area of polygons

Robert Presender rpresender at earthlink.net
Fri Mar 21 10:12:01 EST 2003

```Hi Malte,

I did a Google search for 'polygon'.  This a complicated subject
especially when not regular.

The following URL's are just a few of what is available showing the
complexity.

http://www.cs.unc.edu/~dm/CODE/GEM/chapter.html#Haines94
http://www.cs.man.ac.uk/aig/staff/alan/software/
http://www.mathcats.com/explore/polygons.html
http://www.polygon-weapons.de/

Suggest a survey of the available Google pages (at lease 12) for those
items referencing math polygons.  This may help you decide what
approach you want to take.

On Thursday, March 20, 2003, at 07:46  AM, Malte Brill wrote:

> Hi Bob,
>
>> Yes, these formulae assumes that all sides are of the same length.  If
>> not, a different approach is needed.  Just noted that today's list
>> message 1218 topic 8 from Gernot Lorenz shows a different approach.
>
> It seems working this is all a lot harder as I thought it would be.
>>>> The area of a circumscribed polygon = n(r squared)tan(pi/n) where
>>>> pi =
>>>> 3.14 and
>>>> r = the radius of the circumscribed circle = (l/2)cosec(180/n)
>>
>> Error in above area formula.  Should be: n(r squared)tan(180/n)
> Thanks for correcting this. :-)
>>> This I don´t understand. Does it assume a circle around the polygon?
>>> If so
>>> how could one calculate that circle?
>>
>> Yes it assumes a circle around outside of the polygon(of n sides of
>> equal length).
>> The radius of the circle  is given above: r = (1/2)cosec(180/n)
>> The area of the circle = 3.14(r squared)
>>
>> I can also send you formulae for an inscribed circle (inside of the
>> polygon).
> That would be nice. Even though I haven´t the time to play around with
> polys
> until my current project is finished I would love to try it afterwards.
>>>> Sorry the above is not in strictly math format.. Hope this helps.
>>>> Regards ...  Bob
>
>> If answers to your problem is not sufficient, I would be willing to
>> try
>> to solve it if you can send me a sketch of the polygon(s).
>>
>> Regards ... Bob
>>
> Thanks for that offer. I really appreciate it. :-)
> To be honest. I did not understand all of the discussion on the list.
> So
> actually I haven´t got too far. I guess I need rereading all of the
> post
> quite a few times before I get it.
> If you were willing to set up a small stack showing some different
> approaches to calculaten areas (and perhaps their unions) I would be
> very
> grateful.

I am not that proficient in scripting to do this.  Suggest that you
look at the URLs above and then decide what approach you wish to take.
Maybe some on the list could then provide further help.

>
> Thanks for your support,
>
> Malte
>
>
Regards ...  Bob

```

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