# How to create a smallest quadrilateral concave polygon around GPS points?

I have this GPS track in a metric grid (Symbology by elevation, if anyone wonders):

I need to define it's general area - for registrations and permits, with just 4 points. Therefore, I assume that the corners of a circumscribed quadrilateral polygon (4 lines) will do, as that will be the smallest possible polygon area-wise.

I don't know which Arcmap tools I can use to do it, though I imagine the result should look something like this:

With a polygon I can easily know the corners' coordinates, but if there's another way to extract them, I'm all ears.

Edit: This is the resulting convex hull tool:

• convex hull is something you are looking for? – Naresh Mar 6 '13 at 11:28
• Because your illustration shows that this polygon need not fully enclose the points, the "smallest possible polygon area-wise" will have zero area--and there are many such polygons. Could you please more fully describe the criteria that should apply to identifying a polygon that meets your needs? All you really have told us is that it must have four corners and we can guess it must somehow approximate your GPS points, but we don't yet know exactly how. – whuber Mar 6 '13 at 16:30