Irregular Polygon Area Calculator
Results:
Understanding Irregular Polygons
Area Formulas
Coordinate Method (Shoelace Formula): A = ½|∑(xᵢyᵢ₊₁ - xᵢ₊₁yᵢ)|
Triangulation Method: A = ∑½|xᵢ(yᵢ₊₁ - yᵢ₋₁)|
Coordinate Method Properties
Uses vertex coordinates to calculate area directly
Triangulation Properties
Divides polygon into triangles for area calculation
Vertex Order
Counter-clockwise ordering for positive area
Perimeter and Properties
Perimeter Calculation
Sum of distances between consecutive vertices
P = ∑√[(xᵢ₊₁-xᵢ)² + (yᵢ₊₁-yᵢ)²]
Interior Angles
Sum = (n-2) × 180°
n = number of vertices
Diagonals
Number = n(n-3)/2
Used in triangulation
Applications
Land Surveying
Plot area calculations and boundary mapping
GIS Systems
Geographic data analysis and mapping
Urban Planning
Zoning and land use calculations
Real-World Applications
Geometric Properties
- Centroid Calculation
- Polygon Decomposition
- Convex Hull Analysis
- Interior Point Testing
Computational Methods
- Polygon Triangulation
- Point-in-Polygon Tests
- Boundary Optimization
- Area Partitioning
Real-world Applications
- Property Surveying
- Agricultural Planning
- Construction Layout
- Environmental Assessment