# Area calculations

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<p>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 <br>by the vector-cross-product of vectors along two sides of the triangle sharing a common vertex. <br>For the above mentioned triangle we have three sides as AB, BC and CA, the area of triangle is given by:<br> | <p>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 <br>by the vector-cross-product of vectors along two sides of the triangle sharing a common vertex. <br>For the above mentioned triangle we have three sides as AB, BC and CA, the area of triangle is given by:<br> | ||

Area of Triangle ABC = 1/2 ABS( AB x AC ) ; <br> | Area of Triangle ABC = 1/2 ABS( AB x AC ) ; <br> | ||

- | AB = Vector from vertex A to vertex B <br> | + | AB = Vector from vertex A to vertex B. <br> |

AC = Vector from vertex A to vertex C. <br> | AC = Vector from vertex A to vertex C. <br> | ||

+ | ABS( X ) = function returns absolute value of X. <br> | ||

</p> | </p> | ||

== Area of Polygonal Surface == | == Area of Polygonal Surface == | ||

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

## Revision as of 08:32, 12 September 2005

## 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.

ABS( X ) = function returns absolute value of X.

## 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.