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# Triangle

## Triangle analytical geometry.

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### 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

Triangle Calculator
Pointxy
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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## Citation

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12.8.9

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