# Area calculations

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 Revision as of 01:22, 15 September 2005 (view source)Zxaar (Talk | contribs)← Older edit Latest revision as of 12:31, 19 December 2008 (view source)Peter (Talk | contribs) m (Reverted edits by RoletOchic (Talk) to last version by Zxaar) (2 intermediate revisions not shown) Line 11: Line 11: == Area of Polygonal Surface == == Area of Polygonal Surface ==

A polygon can be divided into triangles sharing a common vertex of the polygon. The total area of the polygon
can be approximated by sum of all triangle-areas it is made up of.

A polygon can be divided into triangles sharing a common vertex of the polygon. The total area of the polygon
can be approximated by sum of all triangle-areas it is made up of.

## Area of Triangle

The area of a triangle made up of three vertices A(x1,y1,z1), B(x2,y2,z2) and C(x3,y3,z3) can be represented
by the vector-cross-product of vectors along two sides of the triangle sharing a common vertex.
For the above mentioned triangle we have three sides as AB, BC and CA, the area of triangle is given by:

$Area\Delta ABC = {1 \over 2}\left| {AB \times AC} \right|$
AB = Vector from vertex A to vertex B.
AC = Vector from vertex A to vertex C.

## Area of Polygonal Surface

A polygon can be divided into triangles sharing a common vertex of the polygon. The total area of the polygon
can be approximated by sum of all triangle-areas it is made up of.