Triangle
Triangle analytical geometry.
Centroid of Triangle
The centroid of a triangle in a coordinate system can be expressed as
x _{ s } = (x_{1} + x_{2}+ x_{3} ) / 3 (1)
y _{ s } = (y_{1} + y_{2}+ y_{3} ) / 3 (1b)
Area of Triangle
The area of the triangle can be expressed as
A =  ((x_{1} y_{2} x_{2}y_{1} ) + (x_{2}y_{3}  x_{3} y_{2}) + (x_{3} y_{1}  x_{1} y_{3} )) / 2  (2)
Triangle Calculator
Point  x  y 

1  
2  
3  
Centroid  
Area 
Example  Centroid and Area of Triangle
The centroid of a triangle with points P_{1} (0,0), P_{2}(1,1) and P_{3} (1,0.5) can be calculated as
x _{ s } = (0 + 1 + 1 ) / 3
= 0.67
y _{ s } = (0 + 1 + 0.5) / 3
= 0.5
The area can be calculated as
A =  ((0 1  1 0) + (1 0.5  1 1) + (1 0  0 0.5)) / 2 
= 0.25
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