Area calculations

(Difference between revisions)
 Revision as of 01:22, 15 September 2005 (view source)Zxaar (Talk | contribs)← Older edit Revision as of 06:17, 3 October 2005 (view source)Zxaar (Talk | contribs) Newer edit → 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.

+ + ---- + Return to [[Numerical methods | Numerical Methods]]

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.