# Area calculations

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== Area of Triangle == | == Area of Triangle == | ||

- | <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 | + | :<math> |

- | AB = Vector from vertex A to vertex B. <br> | + | Area\Delta ABC = {1 \over 2}\left| {AB \times AC} \right| |

- | AC = Vector from vertex A to vertex C. <br> | + | </math> |

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

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

+ | |||

+ | ---- | ||

+ | <i> Return to [[Numerical methods | Numerical Methods]] </i> |

## Latest revision as of 12:31, 19 December 2008

## 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:

**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.

* Return to Numerical Methods *