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# Polygons

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Posted 22 May 2014 - 11:22 PM

Let's define BMAD polygons as polygons where the perimeter and area values are identical.  Does there exist two such polygons (p1, p2) where the number of sides of p1 > the number of sides of p2 but the perimeters are identical?

Edited by BMAD, 22 May 2014 - 11:23 PM.

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### #2 bonanova

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Posted 23 May 2014 - 01:56 AM

Regular?
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Vidi vici veni.

### #3 m00li

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Posted 23 May 2014 - 03:03 AM

Spoiler for if

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Posted 23 May 2014 - 03:22 AM

Regular?

no not necessarily.

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Posted 23 May 2014 - 03:23 AM

Spoiler for if

wouldn't the area be infinitesimally off

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Posted 23 May 2014 - 04:05 AM

For example:

Perimeter = 4 units

Area = 4 units^2

(assuming the above is possible)

Could I find a BMAD Triangle where

Perimeter = 4 units

Area = 4 units^2

assuming the same size unit in both cases

Edited by BMAD, 23 May 2014 - 04:10 AM.

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### #7 witzar

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Posted 23 May 2014 - 09:19 AM   Best Answer

Spoiler for

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Posted 23 May 2014 - 01:26 PM

Does this hold for shapes with sides > 3? >4?

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### #9 m00li

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Posted 23 May 2014 - 10:51 PM

Spoiler for if

wouldn't the area be infinitesimally off

yup, sowwee

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Posted 23 May 2014 - 11:32 PM

nice.

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