# Area calculations

(Difference between revisions)
 Revision as of 05:04, 12 September 2005 (view source)Zxaar (Talk | contribs)← Older edit Revision as of 08:27, 12 September 2005 (view source)Zxaar (Talk | contribs) Newer edit → Line 1: Line 1: - # [[Area of Triangle]] + == Area of Triangle == - # [[Area of Polygonal Surface]] +

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 of Triangle ABC = 1/2 ABS( AB x AC ) ;
+ 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.

## 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 of Triangle ABC = 1/2 ABS( AB x AC ) ;
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.