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Example:Find Triangle Area for given Coordinates of Vertices

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Explanation:

Computing the area of a triangle

 

The area of a triangle can be demonstrated as half of the area of a parallelogram which has the same base length and height.

Calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is:

where b is the length of the base of the triangle, and h is the height or altitude of the triangle. The term 'base' denotes any side, and 'height' denotes the length of a perpendicular from the vertex opposite the side onto the line containing the side itself.

 

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 1/2 times the absolute value of the determinant

For three general vertices, the equation is:

 

(Our solved example in mathguru.com uses this concept).

 

 

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):

 

 

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

 

 

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.