📐 Part 1: Basic Area and Perimeter

1. Calculate the area and perimeter of a rectangle with length 8 cm and width 5 cm.

2. Find the area and perimeter of a square with side length 6 metres.

3. A rectangle has an area of 24 cm² and a width of 4 cm. What is its length and perimeter?

4. Which formula is correct for the area of a rectangle?

A = length + width

A = length × width

A = 2 × (length + width)

A = 4 × side

🔄 Part 2: Unit Conversions

5. Convert the following measurements:

a) 3.5 metres = _______ centimetres

b) 450 centimetres = _______ metres

c) 2.8 kilometres = _______ metres

d) 75 mm = _______ cm

6. A square has a side length of 1.2 metres. Calculate its area in:

a) Square metres: _____________

b) Square centimetres: _____________

7. Convert 5400 cm² to square metres.

📖 Part 3: Word Problems

8. Sarah wants to carpet her rectangular bedroom. The room is 4.5 metres long and 3.2 metres wide. How many square metres of carpet does she need?

9. A farmer has a square paddock with sides of 250 metres. He wants to put a fence around the entire perimeter. How many metres of fencing does he need?

10. The school playground is rectangular with a length of 80 metres and width of 45 metres. The council wants to install new artificial turf that costs $25 per square metre. What will be the total cost?

11. A rectangular swimming pool is 12 metres long and 8 metres wide. The pool needs a safety fence 2 metres away from all edges. What is the perimeter of the fence?

12. Mrs. Johnson's garden is square-shaped with an area of 144 m². She wants to plant flowers along the border. If she plants one flower every 50 cm, how many flowers will she need?

🧠 Part 4: High-Level Challenge Questions

13. Challenge: A rectangular field has a perimeter of 240 metres. If the length is twice the width, find the area of the field.

14. Challenge: Two squares have a combined area of 130 cm². The side of the larger square is 3 cm longer than the side of the smaller square. Find the dimensions of both squares.

15. Challenge: A rectangular piece of land is 150 metres by 200 metres. A square section in one corner measuring 40 metres by 40 metres is reserved for a building. What is the area available for farming?

16. Challenge: The area of a rectangle is 96 cm² and its perimeter is 40 cm. Find the length and width of the rectangle.

17. Challenge: A square and a rectangle have the same perimeter of 32 cm. The rectangle has a length that is 4 cm more than its width. Which shape has the greater area, and by how much?

✏️ Part 5: Drawing and Application

18. Draw and label a rectangle with area 20 cm² and perimeter 18 cm. Show your working to find the dimensions first.

19. Explain in your own words the difference between area and perimeter. Give a real-life example of when you would need to calculate each.

20. A rectangular photo frame has outer dimensions of 30 cm by 20 cm. The frame itself is 3 cm wide all around. What is the area of the photo that fits inside?