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# Polygons

### #1

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.**

### #2

Posted 23 May 2014 - 01:56 AM

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #3

Posted 23 May 2014 - 03:03 AM

### #4

Posted 23 May 2014 - 03:22 AM

Regular?

no not necessarily.

### #5

Posted 23 May 2014 - 03:23 AM

Spoiler for if

wouldn't the area be infinitesimally off

### #6

Posted 23 May 2014 - 04:05 AM

For example:

BMAD Quadrilateral

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.**

### #7

Posted 23 May 2014 - 09:19 AM Best Answer

### #8

Posted 23 May 2014 - 01:26 PM

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

### #9

Posted 23 May 2014 - 10:51 PM

Spoiler for if

wouldn't the area be infinitesimally off

yup, sowwee

### #10

Posted 23 May 2014 - 11:32 PM

nice.

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