Rectangle: length × width
Square: side × side
Triangle: (base × height) ÷ 2
Parallelogram: base × height
Trapezoid: ((base1 + base2) ÷ 2) × height
Circle: π × radius²
Annulus (ring): π × (outer radius² − inner radius²)
Ellipse: π × semi-major axis × semi-minor axis
Regular polygon: (perimeter × apothem) ÷ 2
Irregular polygon (coordinate method): use the shoelace formula
Composite shapes: add areas of parts and subtract cutouts
Sector of a circle: (θ ÷ 360) × π × radius²
Segment of a circle: sector area − triangle area (using radius and central angle)
Annular sector: (θ ÷ 360) × π × (outer radius² − inner radius²)
Cylinder (base area): π × radius²
Sphere (surface area): 4π × radius²
Hemisphere (surface area): 3π × radius²
Quarter circle: (π × radius²) ÷ 4
Right triangle: (base × height) ÷ 2 (use the two perpendicular legs as base and height)