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Re: How to calculate the area of a polygon?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg27724] Re: How to calculate the area of a polygon?
  • From: "Allan Hayes" <hay at haystack.demon.co.uk>
  • Date: Tue, 13 Mar 2001 03:52:42 -0500 (EST)
  • References: <98htbn$mod@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Liwin,

For a polygon with vertices verts= {v1,v2,....vn,v1} (*notice the closing
v1}

The signed area is

(#1.RotateLeft[#2] - RotateLeft[#1].#2)&@@Thread[verts]/2


If  verts is not closes then we can close it.
With your example we get.

verts= Append[#,First[#]]&[{{0,0},{5,0},{10,5},{0,10},{-5,5}}]

        {{0,0},{5,0},{10,5},{0,10},{-5,5},{0,0}}

And the area is

(#1.RotateLeft[#2] - RotateLeft[#1].#2)&@@Thread[verts]/2

175/2

This appoach can be  modified to give swept area.

--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"liwen liwen" <gzgear at yahoo.com> wrote in message
news:98htbn$mod at smc.vnet.net...
> Dear friends,
>
> I want to calculate the area of a polygon, for
> example, the polygon is defined by following points:
> data={{0,0},{5,0},{10,5},{0,10},{-5,5}};
> Regardless of that it is concave or convex.
>
> Any help is appreciated.
>
> Thank you very much!
>
> Liwen   3/11/2001
>
> E-mail:  gzgear at yahoo.com
>
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