Formulae Exploration Worksheet

Year 8 Maths — Measurement & Geometry

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📖 Key Formulae — Reference Guide

💡 Scaffolding tip: Use this box to help you answer questions below. Highlight or circle the formula you need before you start each question.

Perimeter of a rectangle: P = 2l + 2w | Perimeter of a triangle: P = a + b + c

Area of a rectangle: A = l × w | Area of a triangle: A = ½ × b × h

Volume of a rectangular prism: V = l × w × h | Volume of a triangular prism: V = ½ × b × h × length

Units reminder: Area is always in square units (e.g., cm²). Volume is always in cubic units (e.g., cm³).

✏️ Part 1: Formulae Knowledge Check

💡 Scaffolding tip: Look at the Key Formulae box above if you get stuck. Take it one step at a time!

1. Match each term to its correct meaning.

Perimeter

Area

Volume

The amount of 3D space inside a solid shape

The distance around the outside of a shape

The amount of flat surface a 2D shape covers

2. Fill in the missing parts of each formula.

Area of a rectangle: A = _____ × _____

Area of a triangle: A = ½ × _____ × _____

Volume of a rectangular prism: V = _____ × _____ × _____

3. Why does the formula for the area of a triangle include ½? Choose the best explanation.

Because triangles have three sides, so we divide by 2

Because a triangle is half of a rectangle with the same base and height

Because all area formulae use ½

Because the height is always half the base

4. Which formulae use both a base AND a height? Tick ALL that apply.

Perimeter of a rectangle

Area of a triangle

Volume of a triangular prism

Perimeter of a triangle

🔢 Part 2: Substitution Problems

💡 Scaffolding tip: Follow these steps — 1) Write the formula. 2) Substitute the numbers. 3) Calculate. 4) Write the units!

5. A rectangular garden is 8 m long and 5 m wide. Calculate the perimeter and area.

Step 1 — Write the formula for perimeter: P = _______________________

Step 2 — Substitute: P = _______________________

Step 3 — Perimeter = _______ m

Step 4 — Write the formula for area: A = _______________________

Step 5 — Substitute: A = _______________________

Step 6 — Area = _______ m²

6. A triangle has a base of 6 cm and a height of 9 cm. Calculate the area. Show your working.

Area = _______ cm²

7. A rectangular prism (box) has a length of 10 cm, width of 4 cm, and height of 3 cm. Calculate the volume. Show your working.

Volume = _______ cm³

8. A triangular prism has a triangular face with base 5 m and height 4 m. The prism is 12 m long. Calculate the volume. Show your working.

Hint: V = ½ × b × h × length

Volume = _______ m³

9. 🏠 Real-world problem: A school hall floor is rectangular, measuring 25 m by 14 m. New carpet costs $18 per m². How much will it cost to carpet the entire floor?

Hint: First find the area, then multiply by the cost per m².

Total cost = $___________

🌟 Part 3: Extension & Self-Assessment

10. 🚀 Extension Task: A swimming pool has a trapezoidal cross-section. The parallel sides are 2 m and 3 m, and the height of the trapezium is 1.5 m. The pool is 20 m long. Derive a formula for the volume and use it to calculate the pool's volume.

Hint: Area of a trapezium = ½ × (a + b) × h, then multiply by the length for volume.

My formula for volume of this prism: V = _______________________

Volume = _______ m³

11. 💻 Digital Extension: If you changed the length of the rectangular prism in Question 7 to 20 cm (double), what happens to the volume? Explain why using the formula.

12. ✅ Self-Assessment — Tick how confident you feel about each success criterion.

I can explain what perimeter, area, and volume mean:

Not yet — I need more help

Getting there — I understand most of it

Got it — I can explain this clearly

I can substitute values into formulae correctly:

Not yet — I need more help

Getting there — I can do most steps

Got it — I can do this independently

I can apply formulae to solve real-world problems:

Not yet — I need more help

Getting there — with some support