Area is the amount of space inside a 2D shape. Perimeter is the total length of the shape's boundary.
Common Formulas
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle | length Γ width | 2(length + width) |
| Triangle | Β½ Γ base Γ height | a + b + c |
| Circle | Ο Γ rΒ² | 2Οr |
| Trapezoid | Β½(a + b) Γ h | a + b + c + d |
Real-World Uses
Area is used for flooring, painting walls, and lot sizes. Perimeter is used for fencing, trim, and borders.
Same Perimeter, Different Area
Shapes with identical perimeters can enclose very different areas β a key insight in design and packaging. Among all rectangles with a fixed perimeter, a square encloses the most area; among all shapes with a fixed perimeter, a circle encloses the most area of all. This is why round or square-ish floor plans are more material-efficient than long, narrow ones.
Irregular Shape Estimation
For rooms or lots that aren't simple rectangles, break the shape into rectangles and triangles, calculate each piece's area separately, then sum them. This "decomposition" method works for almost any polygon and is standard practice in construction takeoffs and land surveying.