Area of a Polygon

Question

How can the area of an irregular polygon be computed from the coordinates of its vertices?

Goals

• Implement a reliable area calculation for simple polygons.
• Connect coordinate formulas with triangulation, determinants, and integration.

Method

Describe the boundary by listing its vertices in order.

• Draw the polygon and check that the vertices follow one orientation around its boundary.
• Compute signed areas using coordinate products or divide the polygon into triangles.
• Test the method on convex and non-convex examples and compare the results.

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