1. Practical problems! Re-turfing the lawn?
The lawn is rectangular and measures 20 metres by 40 metres. Turf costs £8.50 per m2. How much will it cost to buy the turf?
Re-laying the drive?
The drive is also rectangular and measures 8m by 16m. Each brick is 10cm by 20cm and costs £ How many bricks are needed and what is the total cost?

2. Re-Turfing the Lawn?
The lawn is rectangular and measures 20 m by 40 m. Turf costs £8.50 per m2. How much will it cost to buy the turf ?
How much turf is needed?
Area of lawn = base x height of rectangle 20 40
= m2
Cost of turfing the lawn =
800 x £ 8.50
= £

3. Re-laying the Drive?
The drive is also rectangular and measures 8 metres by 16 metres. Each brick is 20cm by 10cm and costs £ How many bricks will be needed and how much will it cost?
Area of each brick =
1 m2 = 1 m x 1 m
= 100cm x 100cm
= cm2
20 cm x 10 cm
= 200cm2
Area of Drive =
8 m x 16 m
= 128 m2
= 128 x
= cm2

4. Farmer Max The Problem:
Farmer Max needs to create a new grazing area for his animals. He has 50m of fencing, which comes in 1m sections. How can he best construct the fencing to give the animals maximum room?

5. Farmer Max He begins by looking at different rectangles…
Do these fields use 50m of fencing?
Which field gives the largest area for his sheep?

6. Farmer Max
Your turn!
Draw a table to show all the different rectangles that he could make. Remember he only has 50 pieces of fencing (and he uses all of them!). Try to put your results in a logical order. You may find some sketches help you to check your work.
Length (m)
Width (m)
Perimeter (m) 1 24
=50 2 23 …
This activity can be given, with varying amounts of guidance, as an open-ended investigation. Emphasis has been given to a logical trial-and-improvement approach. Adjust the subsequent slides to suit your group.
Add another column to your table to show the area of each rectangle. Which one would be best for Farmer Max?

7. A B C D B2 4cm 3cm 3cm 6cm 42cm2 16cm2 33cm2 48cm2 Hit key or click
for ANSWER

8. A A B C D B2 4cm 3cm 3cm 24cm2 6cm 3cm 9cm2 42cm2 42cm2 16cm2 16cm2

9. A B C D B3 3cm 4cm 2cm 2cm 3cm 2cm 9cm 35cm2 28cm2 16cm2 21cm2
Hit key or click
for ANSWER

10. A B C D B3 3cm 4cm 2cm 2cm 12cm2 12cm2 3cm 2cm 4cm2 9cm 35cm2 28cm2

11. Area of a Compound Shape
Next Slide
6cm
6 x 6
= 36cm2
0.5 x 6 x 6
= 18cm2
6cm
6cm
Total = = 54 cm2

12. Area of a Compound Shape
Next Slide
4cm
Rectangle
7 x 10
= 70 cm2
10cm
Triangle
0.5 x 7 x 4
= 14 cm2
7cm
Total = = 56 cm2

13. A B C D B5 4cm 5cm 3cm 6cm 28cm2 35cm2 45cm2 42.5cm2 Hit key or click
for ANSWER

14. A B C D B5 4cm 10cm2 2cm 6cm 5cm 3cm 18cm2 6cm 28cm2 35cm2 45cm2

15. A B C D B8 4cm 1cm 1cm 6cm 3cm 15cm2 29cm2 20cm2 21cm2
Hit key or click
for ANSWER

16. A B C D B8 4cm 5cm2 1cm 1cm 6cm2 6cm 9cm2 3cm 15cm2 15cm2 29cm2 29cm2

17. Area of a Circle
A = r 2
5cm
A = x 5 x 5
= cm2

18. Area of a Sector of a Circle
Whole Circle
Next Slide
A = r 2
A = x 3 x 3
= cm2
3cm
Divide by 2 = cm2

19. Area of a Sector of a Circle
Whole Circle
Next Slide
A = r 2
A = x 4 x 4
= cm2
8cm
Divide by 2 = cm2

20. Area of a Sector of a Circle
Whole Circle
Next Slide
A = r 2
A = x 8 x 8
= cm2
8cm
Divide by 4 = cm2

21. Chequered cuboid problem
This cuboid is made from alternate purple and green centimetre cubes.
What is its surface area?
Surface area
= 2 × 3 × × 3 × × 4 × 5 =
= 94 cm2
Discuss how to work out the surface area that is green.
Ask pupils how we could write the proportion of the surface area that is green as a fraction, as a decimal and as a percentage.
How much of the surface area is green?
48 cm2

22. Surface area of a cuboid
To find the surface area of a shape, we calculate the total area of all of the faces.
A cuboid has 6 faces.
The top and the bottom of the cuboid have the same area.
Discuss the meaning of surface area. The important thing to remember is that although surface area is found for three-dimensional shapes, surface area only has two dimensions. It is therefore measured in square units.

23. Surface area of a cuboid
To find the surface area of a shape, we calculate the total area of all of the faces.
A cuboid has 6 faces.
The front and the back of the cuboid have the same area.

24. Surface area of a cuboid
To find the surface area of a shape, we calculate the total area of all of the faces.
A cuboid has 6 faces.
The left hand side and the right hand side of the cuboid have the same area.

25. Surface area of a cuboid
To find the surface area of a shape, we calculate the total area of all of the faces.
Can you work out the surface area of this cubiod?
5 cm
8 cm
The area of the top = 8 × 5
= 40 cm2
7 cm
The area of the front = 7 × 5
= 35 cm2
The area of the side = 7 × 8
= 56 cm2

26. Surface area of a cuboid
To find the surface area of a shape, we calculate the total area of all of the faces.
So the total surface area =
5 cm
8 cm
2 × 40 cm2
Top and bottom
7 cm
+ 2 × 35 cm2
Front and back
Stress the importance to work systematically when finding the surface area to ensure that no faces have been left out.
We can also work out the surface area of a cuboid by drawing its net (see slide 51). This may be easier for some pupils because they would be able to see every face rather than visualizing it.
+ 2 × 56 cm2
Left and right side
= = 262 cm2

27. Volume of a prism made from cuboids
What is the volume of this L-shaped prism?
3 cm
We can think of the shape as two cuboids joined together.
3 cm
Volume of the green cuboid
4 cm
= 6 × 3 × 3 = 54 cm3
6 cm
Volume of the blue cuboid
Compare this with slide 50, which finds the surface area of the same shape.
= 3 × 2 × 2 = 12 cm3
Total volume
5 cm
= = 66 cm3

28. Volume of a prism
Remember, a prism is a 3-D shape with the same cross-section throughout its length.
3 cm
We can think of this prism as lots of L-shaped surfaces running along the length of the shape.
Volume of a prism
= area of cross-section × length
If the cross-section has an area of 22 cm2 and the length is 3 cm,
Volume of L-shaped prism =
22 × 3 =
66 cm3

29. What is the volume of this triangular prism?
Volume of a prism
What is the volume of this triangular prism?
7.2 cm
4 cm
5 cm
Area of cross-section = ½ × 5 × 4 =
10 cm2
Volume of prism = 10 × 7.2 =
72 cm3

30. What is the volume of this prism?
Volume of a prism
What is the volume of this prism?
12 m
4 m
7 m
3 m
5 m
Area of cross-section = 7 × 12 – 4 × 3 =
84 – 12 =
72 cm2
Volume of prism = 5 × 72 =
360 m3