GRADE 9 Mathematics MEASUREMENTS – AREA Notes
Mathematics — Measurements
Subtopic: Area (age ~14)
What is area?
Area is the amount of flat (2-dimensional) surface an object covers. We measure area in square units such as cm², m² or mm².
Common units and conversions
- 1 m² = 10,000 cm² (because 1 m = 100 cm so 1 m² = 100×100 cm²)
- 1 cm² = 100 mm²
- 1 hectare (ha) = 10,000 m² (used for land area)
- To convert cm² → m² divide by 10,000. Example: 2,500 cm² = 2,500 ÷ 10,000 = 0.25 m².
Formulas for area (basic plane shapes)
- Square: area = side × side = s²
- Rectangle: area = length × width = l × w
- Triangle: area = 1/2 × base × height = ½ × b × h
- Parallelogram: area = base × height = b × h
- Trapezium/Trapezoid: area = (sum of parallel sides ÷ 2) × height = ((a+b)/2) × h
- Circle: area = π × r² (use π ≈ 3.1416 or 3.14)
- Semicircle: area = (1/2) × π × r²
Visuals (simple diagrams)
Worked examples
Example 1 — Rectangle
Find the area of a classroom that is 6 m long and 4 m wide.
Solution: Area = l × w = 6 × 4 = 24 m².
Find the area of a classroom that is 6 m long and 4 m wide.
Solution: Area = l × w = 6 × 4 = 24 m².
Example 2 — Triangle
A triangular garden has base 8 m and height 5 m. Find its area.
Solution: Area = ½ × b × h = 0.5 × 8 × 5 = 20 m².
A triangular garden has base 8 m and height 5 m. Find its area.
Solution: Area = ½ × b × h = 0.5 × 8 × 5 = 20 m².
Example 3 — Circle
Find the area of a circular water tank with radius 2 m. Use π = 3.14.
Solution: Area = π r² = 3.14 × (2)² = 3.14 × 4 = 12.56 m².
Find the area of a circular water tank with radius 2 m. Use π = 3.14.
Solution: Area = π r² = 3.14 × (2)² = 3.14 × 4 = 12.56 m².
Example 4 — Compound shape
A shape is made of a rectangle 8 m by 3 m with a semicircle of radius 1.5 m attached to one short side. Find total area (use π = 3.14).
Steps:
1) Rectangle area = 8 × 3 = 24 m².
2) Semicircle area = ½ × π r² = 0.5 × 3.14 × (1.5)² = 0.5 × 3.14 × 2.25 ≈ 3.5325 m².
Total ≈ 24 + 3.5325 = 27.5325 m² ≈ 27.53 m².
A shape is made of a rectangle 8 m by 3 m with a semicircle of radius 1.5 m attached to one short side. Find total area (use π = 3.14).
Steps:
1) Rectangle area = 8 × 3 = 24 m².
2) Semicircle area = ½ × π r² = 0.5 × 3.14 × (1.5)² = 0.5 × 3.14 × 2.25 ≈ 3.5325 m².
Total ≈ 24 + 3.5325 = 27.5325 m² ≈ 27.53 m².
Tips & common mistakes
- Always use the correct units and write them (e.g., m²). Don’t confuse linear units (m) with square units (m²).
- For triangles and parallelograms, the height must be perpendicular to the base.
- When dealing with compound shapes, split the shape into basic shapes, find each area, then add (or subtract for holes).
- Be careful converting units before you calculate. Convert lengths first if necessary, then compute area.
Practice questions
- Find the area of a square with side 7 cm.
- A rectangle has length 12 m and width 3.5 m. Find its area in m².
- A triangle has base 10 cm and height 6 cm. Find its area.
- Find the area of a trapezium whose parallel sides are 8 m and 5 m and whose height is 4 m.
- A circular farm has diameter 14 m. Find the area (use π = 22/7).
- Convert 4,500 cm² into m².
- A playground is a rectangle 30 m by 20 m with a circular flower bed (radius 5 m) removed. Find the area of the playground left. Use π = 3.14.
Answers (click to view)
- Square: area = 7² = 49 cm².
- Rectangle: area = 12 × 3.5 = 42 m².
- Triangle: area = ½ × 10 × 6 = 30 cm².
- Trapezium: area = ((8+5)/2) × 4 = (13/2) × 4 = 26 m².
- Circle: radius = 7 m, area = π r² = (22/7) × 7² = (22/7) × 49 = 22 × 7 = 154 m².
- Convert: 4,500 cm² = 4,500 ÷ 10,000 = 0.45 m².
- Playground: rectangle area = 30×20 = 600 m². Circle area = π r² = 3.14×5² = 3.14×25 = 78.5 m². Remaining = 600 − 78.5 = 521.5 m².
Remember: Area formulas are tools — check that dimensions used are perpendicular heights where required, and always keep units consistent.