# Thread: Complex polygon perimeter/area equation

1. ## 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

2. ## 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 $k^2$.

3. ## 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.