📐 Part 1: Understanding the Formulas

1. Complete the area formulas:

Parallelogram: Area = ________ × ________

Trapezium: Area = ________ × ________ ÷ ________

2. Circle the correct statement about parallelogram area:

Area = length × width

Area = base × height

Area = side × side

Area = base × slant height

3. For a trapezium, which measurements do you need? (Check all that apply)

Length of parallel side a

Length of parallel side b

Height (perpendicular distance)

Length of non-parallel sides

🔢 Part 2: Calculating Areas

4. Calculate the area of a parallelogram with base = 8 cm and height = 5 cm.

5. Find the area of a trapezium with parallel sides of 12 m and 8 m, and height of 6 m.

6. A parallelogram has an area of 72 cm². If the base is 9 cm, what is the height?

7. Calculate the area of a trapezium where the parallel sides are 15 cm and 9 cm, and the height is 4 cm.

🏡 Part 3: Real-World Problems

8. Sarah's garden bed is shaped like a parallelogram. The base is 4.5 metres and the height is 2.8 metres. What is the area of her garden bed?

9. A trapezoidal swimming pool has parallel sides of 25 metres and 15 metres. The width of the pool is 8 metres. Calculate the surface area of the pool.

10. A farmer wants to fence a trapezoidal paddock. The parallel sides are 120 m and 80 m long, with a width of 60 m. If fencing costs $12 per square metre, how much will it cost to fence the entire area?

✏️ Part 4: Drawing and Labelling

11. Draw a parallelogram and label the base and height clearly:

12. Draw a trapezium and label both parallel sides (a and b) and the height (h):

13. Explain in your own words why we use perpendicular height (not slant height) when calculating areas:

🧩 Part 5: Challenge Problems

14. A composite shape is made from a rectangle (6 cm × 4 cm) with a triangular section removed from one corner. The triangle has a base of 2 cm and height of 3 cm. What is the remaining area?

15. Match each shape property with its correct description:

1. Parallelogram

2. Trapezium

3. Rectangle

4. Triangle

A. One pair of parallel sides

B. Two pairs of parallel sides, all angles 90°

C. Two pairs of parallel sides

D. Three sides, no parallel sides

16. Extension: If you double both the base and height of a parallelogram, how does this affect the area? Explain your reasoning: