\[A=\frac{\left|x_1y_2+x_2y_3+x_3y_4+x_4y_1-y_1x_2-y_2x_3-y_3x_4-y_4x_1\right|}{2}\]
Variables
Apolygon area
x1x-coordinate of first vertex
y1y-coordinate of first vertex
x2x-coordinate of second vertex
y2y-coordinate of second vertex
x3x-coordinate of third vertex
y3y-coordinate of third vertex
x4x-coordinate of fourth vertex
y4y-coordinate of fourth vertex
Description
What is this formula?
This formula calculates the area of a polygon from the coordinates of its vertices using the Shoelace Formula.
When to use it
Use this formula in coordinate geometry, surveying, GIS, engineering, and computer graphics when polygon vertices are known.
Example
For the vertices:
(1,1)
(5,1)
(4,4)
(1,3)
A = abs((1*1+5*4+4*3+1*1-1*5-1*4-4*1-3*1)/2)
A = 10.5
Applications
- Land surveying
- GIS and mapping
- CAD and computer graphics
- Coordinate geometry
- Engineering calculations