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 = (x_{B}, y_{B})
and C = (x_{C}, y_{C}), 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 = (x_{A}, y_{A}, z_{A}),
B = (x_{B}, y_{B}, z_{B})
and C = (x_{C}, y_{C}, z_{C})}
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.