Rectangle:
  Area = Length × Width
  Example: 15 ft × 12 ft = 180 sq ft

Square:
  Area = Side × Side = Side²
  Example: 10 ft × 10 ft = 100 sq ft

L-Shaped Room:
  Split into two rectangles
  Area = (L₁ × W₁) + (L₂ × W₂)
  Example: (15 × 10) + (8 × 6)
         = 150 + 48 = 198 sq ft

Perimeter:
  P = 2(L + W)
  Example: 2(15 + 12) = 54 ft

Most rooms are rectangular. For L-shapes, T-shapes, or U-shapes, break into rectangles and add areas.

Triangle:
  Area = ½ × Base × Height
  Example: ½ × 20 ft × 15 ft = 150 sq ft

Right Triangle:
  Area = ½ × Leg₁ × Leg₂
  Example: ½ × 8 × 6 = 24 sq ft
  Hypotenuse = √(8² + 6²) = 10 ft

Trapezoid:
  Area = ½ × (Base₁ + Base₂) × Height
  Example: ½ × (20 + 14) × 10
         = ½ × 34 × 10 = 170 sq ft

Heron's Formula (any triangle):
  s = (a + b + c) / 2  (semi-perimeter)
  Area = √(s(s−a)(s−b)(s−c))

Irregular lots often use triangles. Heron's formula works when you know all three sides but not the height.

Circle:
  Area = π × r²
  Example: r = 8 ft
  Area = 3.14159 × 64 = 201.06 sq ft

Semi-circle:
  Area = ½ × π × r²
  Example: r = 6 ft
  Area = ½ × 3.14159 × 36 = 56.55 sq ft

Ellipse:
  Area = π × a × b
  (a = semi-major, b = semi-minor axis)
  Example: a = 12 ft, b = 8 ft
  Area = 3.14159 × 12 × 8 = 301.59 sq ft

Circumference = 2 × π × r
  Example: 2 × 3.14159 × 8 = 50.27 ft

Circular areas appear in patios, pools, round rooms, and curved landscape features. Measure the diameter and divide by 2 for radius.

Strategy: Break into simple shapes

1. Identify rectangles, triangles, circles
2. Measure each section independently
3. Sum all areas (add protruding sections)
4. Subtract cutouts (alcoves, columns)

Example: Room with bay window
  Main rectangle: 20 × 15 = 300 sq ft
  Bay window (trapezoid): 
    ½ × (6 + 4) × 3 = 15 sq ft
  Closet alcove: 4 × 3 = 12 sq ft

  Total = 300 + 15 + 12 = 327 sq ft

For irregular lots:
  Use GPS coordinates or survey data
  Apply Shoelace formula:
  A = ½|Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)|

The Shoelace/Gauss formula calculates area from coordinates — surveyors use GPS points to compute lot areas precisely.