GEOMETRY · 5 min read
Area, Perimeter, and Volume: 2D vs 3D Geometric Formulas
Visual guide to boundaries, surface space, and capacity — from floor tiling to shipping box capacity.
Perimeter vs. Area vs. Volume at a Glance
• Perimeter: 1-dimensional measurement along the boundary edge (measured in linear units: ft, meters, inches).
• Area: 2-dimensional measurement of flat surface space covered (measured in square units: sq ft, m²).
• Volume: 3-dimensional measurement of space enclosed inside a solid (measured in cubic units: cubic yards, liters, m³).
Essential 2D Formulas
Rectangle: Perimeter = 2(length + width) | Area = length × width
Circle: Circumference = 2πr | Area = πr²
Triangle: Area = ½ × base × height
Circle: Circumference = 2πr | Area = πr²
Triangle: Area = ½ × base × height
WORKED EXAMPLE · FLOOR TILING
A room is 14 feet long by 12 feet wide. How many square feet of flooring are required, and what is the baseboard perimeter?
• Flooring Area: 14 ft × 12 ft = 168 sq ft.
• Baseboard Perimeter: 2 × (14 + 12) = 2 × 26 = 52 linear feet.
Essential 3D Volume Formulas
Rectangular Prism (Box): Volume = length × width × height
Cylinder: Volume = πr² × height
Sphere: Volume = 4/3 × πr³ | Surface Area = 4πr²
Cylinder: Volume = πr² × height
Sphere: Volume = 4/3 × πr³ | Surface Area = 4πr²
WORKED EXAMPLE · GARDEN SOIL IN CUBIC YARDS
A raised garden bed is 12 ft long, 6 ft wide, and 1.5 ft deep. How many cubic yards of soil are needed?
1. Calculate cubic feet: 12 × 6 × 1.5 = 108 cubic feet.
2. Convert to cubic yards (1 yard = 3 feet, so 1 cubic yard = 3³ = 27 cubic feet):
108 ÷ 27 = 4.0 cubic yards of topsoil.
Geometry and measurement tools:
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