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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