MEASUREMENT — Area

Subject: Mathematics  |  Subtopic: Area  |  Target age: 12 years (Kenya)

What is area?

Area is the amount of space inside a flat shape. We measure area by counting how many unit squares (for example, 1 cm² or 1 m²) fit inside the shape.

Common units of area

• Square millimetre (mm²)
• Square centimetre (cm²)
• Square metre (m²) — common for rooms and classrooms
• Hectare (ha) — used for land; 1 ha = 10,000 m²
• Square kilometre (km²) — for very large areas

Important conversions

• 1 m = 100 cm → 1 m² = 100 cm × 100 cm = 10,000 cm²
• 1 cm = 10 mm → 1 cm² = 10 mm × 10 mm = 100 mm²
• 1 ha = 10,000 m²
• 1 km² = 1,000,000 m²

Area by shape — formulas and examples

1. Rectangle

Formula: Area = length × width

2. Square

Formula: Area = side²

Example: A square tile has side 50 cm. Area = 50 × 50 = 2500 cm².

3. Triangle

Formula: Area = 1/2 × base × height

Example: Base = 8 m, height = 5 m. Area = 1/2 × 8 × 5 = 4 × 5 = 20 m².

4. Parallelogram

Formula: Area = base × height (height is perpendicular to the base)

Example: Base = 7 m, height = 3 m. Area = 7 × 3 = 21 m².

5. Trapezium (Trapezoid)

Formula: Area = 1/2 × (sum of parallel sides) × height

Example: Parallel sides = 10 m and 6 m, height = 4 m. Area = 1/2 × (10+6) × 4 = 1/2 × 16 × 4 = 8 × 4 = 32 m².

6. Circle

Formula: Area = π × r². Use π ≈ 3.14 or π = 22/7 where appropriate.

Example: Radius = 3 m. Area ≈ 3.14 × 3² = 3.14 × 9 = 28.26 m².

Working with compound shapes

If a shape is made of two or more simple shapes, split it into parts (rectangles, triangles, etc.), find each area, then add or subtract as needed.

Example: A garden is a rectangle 12 m by 8 m with a triangular flower bed of base 4 m and height 3 m removed. Garden area = rectangle − triangle = (12×8) − (1/2×4×3) = 96 − 6 = 90 m².

Examples with unit conversion

1) Convert 0.75 hectare to square metres.

1 ha = 10,000 m² → 0.75 ha = 0.75 × 10,000 = 7,500 m².

2) A plot is 1500 m². How many hectares is it?

1 ha = 10,000 m². So hectares = 1500/10,000 = 0.15 → 0.15 ha.

Helpful tips

• Always check that length and height are in the same units before calculating area.
• Label the units in your final answer (e.g., m², cm²).
• For circle area questions in KCPE/KCSE style, use π = 3.14 or 22/7 as the question tells you.
• Practice sketching shapes and marking base and height clearly.

Practice questions

1. A rectangle is 9 m by 5 m. Find its area.
2. A triangle has base 10 cm and height 6 cm. Find its area.
3. A circular water tank has radius 2 m. Find the area of the circle (use π = 3.14).
4. A field is 0.25 ha. What is its area in m²?
5. A compound shape: rectangle 14 m by 6 m with a semicircle (radius 3 m) attached on one short side. Find total area (use π = 3.14). Hint: semicircle area = 1/2 πr².

Answers

1. 9 × 5 = 45 m².
2. 1/2 × 10 × 6 = 5 × 6 = 30 cm².
3. Area = 3.14 × 2² = 3.14 × 4 = 12.56 m².
4. 0.25 ha = 0.25 × 10,000 = 2,500 m².
5. Rectangle = 14 × 6 = 84 m². Semicircle: 1/2 × 3.14 × 3² = 0.5 × 3.14 × 9 = 14.13 m². Total ≈ 84 + 14.13 = 98.13 m².

Remember: Area tells you how much flat space a shape covers. Practise by counting unit squares and by using formulas for different shapes.

Good luck — keep practising!