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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