Ideas in this flowchart

• Trapezoidal algorithm for irregular polygons
• The polygon is divided conceptually into trapezoids.
• The division uses coordinate pairs of the vertices in a Cartesian system.
• The trapezoid areas are calculated and summed.
• Negative contributions help remove areas outside the polygon.
• The vertices must be ordered consistently for the negative contributions to work correctly.
• The algorithm can be performed by hand.
• Implementation in software is more efficient.
• Spreadsheets can implement the algorithm.
• Programming environments can implement the algorithm.
• GIS software can implement the algorithm.