# Area calculations

(Difference between revisions)
 Revision as of 05:04, 12 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) (7 intermediate revisions not shown) 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:
+ :$+ Area\Delta ABC = {1 \over 2}\left| {AB \times AC} \right| +$ + '''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.

## 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.