# Triangle

### Centroid of Triangle

The centroid of a triangle in a co-ordinate 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*can be calculated as

_{3}(1,0.5)* 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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