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Application of Determinants:Find Area

 Post to:   Explanation:

Triangle

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ABC.

## Computing the area of a triangle

### Using coordinates

If vertex A is located at the origin (0, 0) of a Cartesian coordinate system and the coordinates of the other two vertices are given by B = (xByB) and C = (xCyC), then the area can be computed as � times the absolute value of the determinant For three general vertices, the equation is:  In three dimensions, the area of a general triangle {A = (xAyAzA), B = (xByBzB) and C = (xCyCzC)} is the Pythagorean sum of the areas of the respective projections on the three principal planes (i.e. x = 0, y = 0 and z = 0): (Our solved example in mathguru.com uses this concept)

http://en.wikipedia.org/wiki/Triangle