📚 Part 1: Multiple Choice

1. What is the formula for the area of a triangle?

A = base × height

A = ½ × base × height

A = 2 × base × height

A = base + height

2. A rectangle has a length of 8 metres and a width of 5 metres. What is its area?

13 m²

26 m²

40 m²

80 m²

3. Which of the following polygons have the same area formula? (Select all that apply)

Square

Rectangle

Parallelogram

Triangle

4. A trapezium has parallel sides of 6 cm and 10 cm, with a height of 4 cm. What is its area?

24 cm²

32 cm²

40 cm²

64 cm²

✏️ Part 2: Problem Solving

5. Calculate the area of a parallelogram with base 12 metres and height 7 metres. Show your working.

6. A triangle has a base of 15 cm and an area of 60 cm². What is the height of the triangle?

7. Find the area of a rhombus with diagonals measuring 8 metres and 6 metres.

Formula: Area of rhombus = ½ × d₁ × d₂

8. A regular hexagon can be divided into 6 equilateral triangles. If each triangle has an area of 9 cm², what is the total area of the hexagon?

🎯 Part 3: Real-World Applications

9. Sarah wants to paint a triangular wall in her bedroom. The wall has a base of 4 metres and a height of 3 metres. If one litre of paint covers 8 m², how much paint will she need?

10. A farmer has a rectangular paddock that is 50 metres long and 30 metres wide. He wants to plant grass seed that costs $2.50 per square metre. What will be the total cost?

11. Complete the following formula:

Area of trapezium = ½ × (______ + ______) × ______

12. Explain in your own words why the area formula for a triangle includes "½".