# 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 *

## Related Topics

### • Mathematics

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

## Related Documents

### Beam Loads - Support Force Calculator

Calculate beam load and supporting forces.

### Cartesian Coordinate System - Distance and Intermediate Position Between Two Points

Distance and intermediate position between two point in a cartesian x and y coordinate system.

### Center of Gravity

A body and the center of gravity.

### Complex Numbers

Complex numbers are used in alternating current theory and mechanical vector analysis.

### Law of Cosines

One side of a triangle when the opposite angle and two sides are known.

### Law of Sines

Calculate the angles in a generic triangle.

### Law of Tangents

Triangles and law of tangents.

### Miter Saw - Calculate Sawing Angle

Calculate miter saw protractor angles for skirting and decorative mouldings work.

### Oblique Triangle

Calculate oblique triangles.

### Polar vs. Cartesian Coordinates

Convert between Cartesian and Polar coordinates.

### Pythagorean Theorem

Verifying square corners.

### Radians vs. Degrees

Radian is the SI unit of angle. Convert between degrees and radians. Calculate angular velocity.

### Right Angled Triangle

Right angled triangle equations.