Mathematics — Measurements

Subtopic: Area (for age 11)

What is area? — Area is the amount of space inside a flat shape (a region on a plane). We measure area using square units such as square centimetres (cm²) and square metres (m²).

Important units

• Square centimetre: cm² (used for small shapes)
• Square metre: m² (used for rooms, fields)
• Conversion: 1 m² = 10 000 cm²

Basic area formulas

• Rectangle: Area = length × width (A = l × w)
• Square: Area = side × side (A = s²)
• Triangle: Area = 1/2 × base × height (A = 1/2 × b × h)
• Parallelogram: Area = base × height (A = b × h)
• Trapezium (trapezoid): Area = 1/2 × (sum of parallel sides) × height (A = 1/2 × (a + b) × h)

Visual examples

Worked examples

1. A rectangular classroom is 7 m long and 6 m wide. Find its area.
   A = l × w = 7 m × 6 m = 42 m².
2. A triangular garden has base 4 m and height 3 m. Find its area.
   A = 1/2 × b × h = 1/2 × 4 m × 3 m = 6 m².
3. Convert 2 400 cm² into m².
   1 m² = 10 000 cm². So 2 400 cm² = 2 400 ÷ 10 000 = 0.24 m².

Tips

• Always use the same units for length and width before multiplying (change cm to m if needed).
• Write the unit after your answer (for example, m² or cm²).
• For triangles, the height must be at right angles (perpendicular) to the base.

Practice questions (try these)

1. A playground is 12 m long and 9 m wide. Find its area.
2. A square tile has side 25 cm. What is its area in cm²?
3. A trapezium has parallel sides 8 m and 5 m with height 4 m. Find the area.
4. Draw a triangle with base 6 cm and height 4 cm, then calculate its area.

These notes follow simple Kenyan school measures and standard metric units. Ask your teacher if you need more examples or help with drawing accurate shapes.