Rectangle Formulas
A rectangle is a four-sided polygon (quadrilateral) where every interior angle equals 90°. Opposite sides are equal and parallel, making it one of the most common shapes in everyday life — rooms, screens, doors, books, and tiles are all rectangles.
Area A = Length × Width = l × w
Perimeter P = 2 × (Length + Width) = 2(l + w)
Diagonal d = √(l² + w²) (from Pythagorean theorem)
Perimeter P = 2 × (Length + Width) = 2(l + w)
Diagonal d = √(l² + w²) (from Pythagorean theorem)
Worked Examples
Example 1 – Room Floor
A rectangular room is 8 m long and 5 m wide. Calculate its area (for flooring) and perimeter (for skirting boards).
Area = 8 × 5 = 40 m²
Perimeter = 2 × (8 + 5) = 2 × 13 = 26 m
Diagonal = √(8² + 5²) = √(64 + 25) = √89 ≈ 9.43 m
Perimeter = 2 × (8 + 5) = 2 × 13 = 26 m
Diagonal = √(8² + 5²) = √(64 + 25) = √89 ≈ 9.43 m
Example 2 – Garden Plot
A rectangular garden measures 12 m × 7 m. How much fencing is needed?
Perimeter = 2(12 + 7) = 2 × 19 = 38 m of fencing
Area = 12 × 7 = 84 m² of lawn
Area = 12 × 7 = 84 m² of lawn
Example 3 – Screen Size
A monitor is 40 cm wide and 30 cm tall. Find its area and diagonal.
Area = 40 × 30 = 1200 cm²
Diagonal = √(40² + 30²) = √(1600 + 900) = √2500 = 50 cm (≈ 19.7 inch screen)
Diagonal = √(40² + 30²) = √(1600 + 900) = √2500 = 50 cm (≈ 19.7 inch screen)
Rectangle vs Square vs Parallelogram
| Shape | All angles 90°? | All sides equal? | Area Formula |
|---|---|---|---|
| Rectangle | ✅ Yes | ❌ No (opposite equal) | l × w |
| Square | ✅ Yes | ✅ Yes | s² |
| Parallelogram | ❌ No | ❌ No (opposite equal) | b × h |
A square is a special rectangle where length = width. All squares are rectangles, but not all rectangles are squares.
Real-World Applications
- Construction & flooring: Calculate how many tiles, planks, or carpet rolls are needed based on room area
- Gardening: Determine the amount of grass seed, fertilizer, or compost needed per m²
- Painting: Estimate wall area (length × height) to determine how many cans of paint to buy
- Screen technology: Monitors, phones, and TVs are specified by diagonal but area determines usable display space
- Agriculture: Farm field areas are calculated as rectangles for crop planning and yield estimates
- Packaging: Box surface area = sum of 6 rectangle faces, used to calculate material needed
Finding Missing Dimensions
You can rearrange the formulas to find unknown dimensions:
If you know Area and Length: Width = Area ÷ Length
If you know Perimeter and Length: Width = (Perimeter ÷ 2) − Length
Example: Area=60m², Length=10m → Width = 60÷10 = 6m
If you know Perimeter and Length: Width = (Perimeter ÷ 2) − Length
Example: Area=60m², Length=10m → Width = 60÷10 = 6m