Area - Measuring Two-Dimensional Space
Area is the amount of two-dimensional space inside a flat shape or surface. We use it every day – measuring floor space before buying tiles, calculating how much paint a wall needs, or finding the size of a garden.
What Is Area?
Area is measured in square units. If you cover a shape with unit squares, the number of squares needed is the area. The unit must match the linear units used: centimetres give cm², metres give m².
Units of Area
| Unit | Symbol | Relation | Typical use |
|---|---|---|---|
| Square millimetre | mm² | 100 mm² = 1 cm² | Very small surfaces |
| Square centimetre | cm² | 10,000 cm² = 1 m² | Paper, small tiles |
| Square metre | m² | Base unit | Rooms, floor area |
| Hectare | ha | 1 ha = 10,000 m² | Agricultural land, parks |
| Square kilometre | km² | 1 km² = 100 ha | Countries, large regions |
Area Formulas
| Shape | Formula | Variables |
|---|---|---|
| Rectangle | A = l × w | l = length, w = width |
| Square | A = s² | s = side length |
| Triangle | A = ½ × b × h | b = base, h = perpendicular height |
| Circle | A = πr² | r = radius |
| Parallelogram | A = b × h | b = base, h = perpendicular height |
| Trapezium | A = ½(a + b) × h | a, b = parallel sides, h = height |
Worked Examples
Find the area of a room 6 m x 4.5 m.
A = 6 × 4.5 = 27 m².
A triangular garden has base 12 m and height 7 m. Find its area.
A = ½ × 12 × 7 = 42 m².
Convert 3.5 ha to m².
3.5 × 10,000 = 35,000 m².
A circular pond has radius 4 m. Find its area to 2 decimal places.
A = π(4)² = 16π ≈ 50.27 m².
Key Takeaways
- Area is measured in square units: mm², cm², m², ha, km².
- 1 m² = 10,000 cm² | 1 ha = 10,000 m² | 1 km² = 100 ha.
- Always use the perpendicular height in area formulas, not the slant height.
Practice Questions
- Find the area of a rectangle 9 m x 6.5 m.
- A circle has diameter 14 cm. Find its area to 2 decimal places.
- A trapezium has parallel sides 8 m and 5 m, and height 6 m. Find its area.
- Convert 45,000 m² to hectares.
- A square carpet has area 16 m². What is the length of each side?