Core answer: Rectangle area = length × width; perimeter = 2(length + width); diagonal = √(l² + w²). A 4 × 2.5 m room is 10 m² with 13 m of perimeter and a 4.72 m diagonal. Squares are the special case: for a fixed perimeter, the square maximizes area — the math behind every "efficient shape" argument.
The three formulas
| Quantity | Formula | Example (5 m × 3 m) |
|---|---|---|
| Area | A = l × w | 15 m² |
| Perimeter | P = 2(l + w) | 16 m |
| Diagonal | d = √(l² + w²) | 5.83 m |
Worked examples
Example 1 — Flooring. A 4.2 × 3.6 m room = 15.12 m². Laminate packs cover 2.4 m²; with 8% cutting waste you need 15.12 × 1.08 / 2.4 ≈ 6.8 → buy 7 packs.
Example 2 — Baseboards. Same room, one 0.9 m door: perimeter 15.6 − 0.9 = 14.7 m of baseboard; buy 15–16 m.
Example 3 — TV sizing. A "55-inch" TV is the *diagonal*. A 16:9 screen has width ≈ 0.8716 × diagonal ≈ 48 in (122 cm) and height ≈ 27 in (68 cm) — check it fits the cabinet, not just the wall.
The square-maximizes-area fact
Fixed perimeter 40 m: 12 × 8 gives 96 m², 10 × 10 gives 100 m², 15 × 5 gives 75 m². The square always wins — the reason pasture fences, floor tiles, and IC dies tend toward square when material is the constraint. Conversely, for fixed area, the square *minimizes* perimeter — cheapest fencing.
Common mistakes and myths
- Mixing units — 1.2 m × 80 cm: convert first (1.2 × 0.8 = 0.96 m²); never multiply mixed units.
- Confusing area and perimeter — doubling both dimensions doubles perimeter but quadruples area; paint scales with area, skirting with perimeter.
- Forgetting waste in materials — diagonal layouts and pattern matching need 10–15% extra, not 5%.
- Assuming "bigger room = much more perimeter" — perimeter grows linearly with scale while area grows quadratically; big rooms need proportionally less trim per m² of floor.
- Diagonal ≠ l + w — a 3-4 rectangle's diagonal is 5, not 7; Pythagoras, not addition.