VCE VCE VM Numeracy (Year 11) · Unit 1 — Number, Shape, Quantity and Measures, Relationships · 12m read

Shape — Area, Perimeter and Volume for Real Jobs

Trades and DIY jobs all start with measuring. Getting area and volume right saves money and trips to the hardware store.

Learning objective: Calculate perimeter, area and volume to estimate materials for practical tasks such as painting, tiling and landscaping.

By the end of this lesson you can:

• I can calculate perimeter and area of rectangles, triangles and circles.
• I can calculate volume of prisms and cylinders.
• I can add a waste allowance and round up to whole units.

Measure twice, cut once. Tradespeople double-check measurements before cutting or ordering. A small error can waste a lot of material.

Formulas in words

PERIMETER — distance around the edge (add all sides).
AREA
• Rectangle: length × width.
• Triangle: ½ × base × height.
• Circle: π × r² (use π ≈ 3.14 or π ≈ 22/7 — both are accepted and give answers in the same ballpark).
VOLUME
• Rectangular prism: length × width × height.
• Cylinder: π × r² × height.
• 1 m³ = 1000 L.

PRACTICAL RULES
• Add a waste allowance (often 10%) for tiles, flooring and timber.
• Round UP to whole units — you cannot buy 5.7 boxes.

Worked example (Medium)

A floor is 3 m × 2.5 m. Tiles come in boxes covering 1.44 m². Allow 10% waste. How many boxes are needed?

1. Area. 3 × 2.5 = 7.5 m².
2. Add waste. 7.5 × 1.1 = 8.25 m².
3. Boxes. 8.25 ÷ 1.44 ≈ 5.73.
4. Round up. 6 boxes.

Answer: 6 boxes of tiles.

Worked example (Medium)

A round garden bed has a radius of 1.4 m. Find its area.

1. With π ≈ 22/7. 22/7 × 1.4 × 1.4 = 22/7 × 1.96 = 6.16 m².
2. With π ≈ 3.14. 3.14 × 1.96 ≈ 6.15 m².

Answer: About 6.2 m² — both approximations of π are acceptable and give almost the same answer.

Common mistakes

• Using diameter instead of radius Area uses radius squared. Fix: Halve the diameter first.
• Rounding down materials You will run short. Fix: Always round up.

Practice questions

1. The area of a triangle with base 6 m and height 4 m is:

   1. 24 m²
   2. 12 m²
   3. 10 m²
   4. 20 m²

   (1 marks)

2. A wall is 5 m × 2.7 m and needs two coats. One litre of paint covers 16 m². How many litres should you buy?

   (2 marks)

3. A rainwater tank is a cylinder with radius 1 m and height 2 m. How many litres does it hold?

   (2 marks)

Summary

• Area: rectangle l × w; triangle ½bh; circle πr².
• Volume: prism l × w × h; cylinder πr²h.
• π ≈ 3.14 or 22/7 — both accepted.
• Add waste and round up.