# Triangle

## Triangle analytical geometry

### Centroid of Triangle

The centroid of a triangle in a co-ordinate system can be expressed as

xs = (x1 + x2 + x3) / 3                        (1)

ys = (y1 + y2 + y3) / 3                        (1b)

### Area of Triangle

The area of the triangle can be expressed as

A = | ((x1 y2 - x2 y1) + (x2 y3 - x3 y2) + (x3 y1 - x1 y3)) / 2 |                           (2)

Pointxy
1
2
3
Centroid
Area

### Example - Centroid and Area of Triangle

The centroid of a triangle with points P1(0,0), P2(1,1) and P3(1,0.5) can be calculated as

xs = (0 + 1 + 1) / 3

= 0.67

ys = (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

## Related Topics

• Mathematics - Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more

## Search the Engineering ToolBox

- "the most efficient way to navigate!"

## Engineering ToolBox - SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your SketchUp model with the Engineering ToolBox - SketchUp Extension/Plugin - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

Translate the Engineering ToolBox!