Calculating Square Footage of an Irregular 9-Sided Area

To find the area of an asymmetrical polygon (9 sides), decompose it into simple shapes—triangles, rectangles, trapezoids—calculate each, and sum the results.

Step-by-Step Method

1. Sketch the area to scale on graph paper or use a digital tool (Google Earth, CAD, GIS).
2. Draw diagonals from one vertex to all non-adjacent vertices, creating triangles. Alternatively, enclose the shape in a rectangle and subtract the external triangles.
3. Measure each triangle’s base and height (perpendicular to that base).
4. Apply the triangle area formula: Area = ½ × base × height.
5. For any rectangular or trapezoidal sections, use:
   • Rectangle: Area = base × height
   • Trapezoid: Area = ½ × height × (base₁ + base₂)
6. Sum all sub-areas for the total square footage.

Formulas Reference

• Triangle: A = 0.5 × b × h
• Parallelogram: A = b × h
• Rhombus (diagonals d₁, d₂): A = 0.5 × d₁ × d₂
• Trapezoid: A = 0.5 × h × (b₁ + b₂)
• Regular polygon (apothem a, perimeter P): A = 0.5 × a × P

For volume calculations (e.g., cut/fill), use the Average End Area method: slice the area into parallel cross-sections, compute each section’s area, average adjacent pairs, multiply by the distance between sections, and sum. A spreadsheet simplifies this.