Results 1 to 3 of 3

Math Help - Complex polygon perimeter/area equation

  1. #1
    Newbie
    Joined
    Jun 2012
    From
    Jackson, MI
    Posts
    2

    Complex polygon perimeter/area equation

    Hi. What I'm looking to do is probably impossible with only the given data, but I've come here to make certain before giving up!

    I have a non-regular polygon with several concave and convex characteristics. I know the number of sides, the lengths of each side (therefore the total perimeter as well), and the area of the polygon. I do no, however, know the locations of each side, nor what the polygon actually looks like.

    Is it possible to calculate the new area of the polygon if its perimeter is offset outward by a certain factor. (i.e., each side would be shifted perpendicularly to its length outward by a specified amount.)

    I want to say no, based on the sheer number of unknowns, but there's this nagging feeling that says there must be a general correlation between area, perimeter, and # of sides (the polygon's complexity).

    Any help is appreciated!

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: Complex polygon perimeter/area equation

    Yes. If the sides of the polygon are scaled by a constant k, the perimeter is multiplied by k and the area is multiplied by k^2.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2012
    From
    Jackson, MI
    Posts
    2

    Re: Complex polygon perimeter/area equation

    richard1234, thanks for the reply. If I were scaling the polygon as a whole, or if it were a regular polygon, that'd be great.

    Unfortunately, the scenario I'm describing offsets each side by the specified distance. If you're familiar with any CAD software, this would be an offset command, not a scale command. For example, in concave conditions (such as a U or C shape), the offset sides of the polygon would be moving toward each other. So, although the sides are being offset perpendicularly by the same distance, some sides might actually decrease in length.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Polynomial, area of a polygon
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 12th 2011, 11:28 AM
  2. Replies: 3
    Last Post: March 16th 2011, 09:48 AM
  3. Complex- area enclosed by a polygon
    Posted in the Differential Geometry Forum
    Replies: 15
    Last Post: May 7th 2009, 08:24 AM
  4. Area of a polygon
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 22nd 2007, 03:12 PM
  5. Area of a Regular Polygon
    Posted in the Algebra Forum
    Replies: 5
    Last Post: August 2nd 2006, 09:31 PM

Search Tags


/mathhelpforum @mathhelpforum