1. Simple Perimeter, Area and Volume
Grades 1-3

2. To calculate simple perimeter, area and volume @home.
Lesson Objective
To calculate simple perimeter, area and
Success Criteria
Calculate perimeter of 2D shapes, including:
Circumference of circles
Area of circles and composite shapes
Volume of cuboids (by counting)

3. Garden Design Use the garden plan to find the: total area of patio;
Key:
Use the garden plan to find the:
total area of patio;
perimeter of the flower bed;
perimeter around the garden;
fraction of garden area that is not patio or grass.
Shed
Flowerbed
Pond
Patio
Grass
1m2
Click to enlarge
Challenge:
Grass turf can either be bought as:
1 metre squares
£16.45/square
3m × 5m
£105
How many metre squares would you need?
If you bought the 3m × 5m turf, how much grass would be wasted?
Which is the cheapest option?

4. Garden Design Answers Use the garden plan to find the:
Key:
Use the garden plan to find the:
total area of patio; 29m2
perimeter of the flower bed; = 14m
perimeter around the garden; = 32m
fraction of garden area that is not patio or grass.
Shed
Flowerbed
Pond
Patio
Grass
1m2
Area that is not grass or patio = 16m2
Area that is grass and patio = = 37m2
Total area = 37m m2 = 53 m2
Fraction of garden not patio or grass = 16 53

5. Garden Design Answers Challenge: Grass turf can either be bought as:
Key:
Shed
Flowerbed
Pond
Patio
Grass
1m2
1 metre squares
£16.45/square
3m × 5m
£105
How many metre squares would you need? 8
If you bought the 3m × 5m turf, how much grass would be wasted?
15 − 8 = 7m2
Which is the cheapest option?
8 × = £ so the 3 × 5 turf at £105 would be cheaper.

6. Bathroom Design Use the bathroom plan to find out:
323cm
416cm
197cm
21cm
85cm
146cm
209cm
Use the bathroom plan to find out:
how much skirting board you need to go all the way around the bathroom;
the total floor area of the bathroom. Give your answer in m2.
Click to enlarge
Challenge
The builder says:
“If you want floor tiles, you need to buy 90% of the total floor area.”
How much will the tiles cost if they are £16 per square metre?
“To buy vinyl, you need to use the maximum values of length and width so it arrives in one piece. It will then be cut to the shape of the room.”
What fraction of vinyl will be cut away and discarded? (use numbers to 1 d.p.)

7. Bathroom Design Answers
323cm
Use the bathroom plan to find out:
how much skirting board you need to go all the way around the bathroom;
the total floor area of the bathroom. Give your answer in m2.
197cm
416cm
21cm
85cm
146cm
134cm
Missing measurement = 416 – ( ) = 134cm
209cm
missing measurement!
Skirting board:
= 1531cm
Floor Area:
(3.23 × 1.97) + (0.85( )) + (2.09 × 1.34)
= = 12.18m2

8. Bathroom Design Answers
323cm
Challenge
The builder says:
“If you want floor tiles, you need to buy 90% of the total floor area.”
How much will the tiles cost if they are £16 per square metre?
197cm
416cm
21cm
85cm
146cm
Cost: × × 16 = £175.39 90
100
134cm
209cm
Max area = ( ) × = = 14.8m2 to 1 d.p.
Area discarded = (1.34 × 1.46) + (0.21 × 1.97) = = 2.4m2 to 1 d.p.
Fraction of vinyl discarded = = (approx.)
“To buy vinyl, you need to use the maximum values of length and width so it arrives in one piece. It will then be cut to the shape of the room.”
What fraction of vinyl will be cut away and discarded? (use numbers to 1 d.p.)
2.4
14.8 6 37

9. Happy Birthday Granny! Birthday Cake Design
The gap between the photo and the cake circumference is uniform all the way round.
Birthday Cake Design
It’s granny’s Birthday! Calculate the area and circumference of the decoration photograph (to 1 decimal place) if:
the diameter of the cake is 15cm and the gap between the photo and cake circumference is 2cm;
the radius of the cake is 11cm and the gap between the photo and cake circumference is 2.5cm;
the diameter of the cake is 13cm and the gap between the photo and cake circumference is 1.3cm but the cake is also cut in half.
Click to enlarge
Challenge
For each of the questions above, calculate what proportion of the cake’s top area is visible (with just the photo on top).

10. Birthday Cake Design Answers
It’s granny’s Birthday! Calculate the area and circumference of the decoration photograph (to 1 decimal place) if:
the diameter of the cake is 15cm and the gap between the photo and cake circumference is 2cm;
the radius of the cake is 11cm and the gap between the photo and cake circumference is 2.5cm;
the diameter of the cake is 13cm and the gap between the photo and cake circumference is 1.3cm but the cake is also cut in half.
Radius of photograph = (15 − 4) ÷ 2 = 5.5 Area of photograph = πr2 = π × 5.52 = 95.0cm2 to 1 d.p. Circumference of photograph = 2πr = π ×11 = 34.6cm to 1 d.p.
Radius of photograph = (11 − 2.5) = 8.5 Area of photograph = πr2 = π × 8.52 = 227.0cm2 to 1 d.p. Circumference of photograph = 2πr = π ×17 = 53.4cm to 1 d.p.
Radius of photograph = (13 − 2.6) ÷ 2 = 5.2 Area of photograph = ½πr2 = π × 5.22 × ½ = 84.9cm2 to 1 d.p. Circumference of photograph = πr = π × = 26.7cm to 1 d.p.

11. Birthday Cake Design Answers
Challenge
For each of the questions above, calculate what proportion of the cake’s top area is visible (with just the photo on top).
Area of cake = πr² = π × 7.5² = 176.7cm² to 1 d.p. Area of photograph = 95.0cm² to 1 d.p. Fraction of cake visible = = 0.46
176.7
Area of cake = πr² = π × 11² = 380.1cm² to 1 d.p. Area of photograph = 227.0cm² to 1 d.p. Fraction of cake visible = = 0.40
380.1
Area of cake = ½πr² = π × 7.5² × ½ = 88.4cm² to 1 d.p. Area of photograph = 84.9cm² to 1 d.p. Fraction of cake visible 88.4 – 84.9 = = 0.04
88.4

12. Fish Feature = 1cm3
Volume = ………… cm3
Cat Climb = 1m3 (lucky cat!)
Volume = ………… m3
Rat Run = 1in3
Volume = ………… in3
Pet Accessory Design
Use the isometric designs to find the volume of each pet accessory.
Click to enlarge
Fish Feature = 1cm3
Volume = ………… cm3
Cat Climb = 1m3 (lucky cat!)
Volume = ………… m3
Rat Run = 1in3
Volume = ………… in3
Challenge
When you go to buy the cubes for the rat run, you take the design to show the shopkeeper. They try to sell you more cubes than you need and insist they are included in the design.
Why?
How many more cubes could they try to sell you?
What could you do to prove them wrong?

13. Pet Accessory Design Answers
Use the isometric designs to find the volume of each pet accessory.
Cat Climb = 1m3 (lucky cat!)
Volume = 13m3
Rat Run = 1in3
Volume = 18in3
Fish Feature = 1cm3
Volume = 15cm3

14. Pet Accessory Design Answers
Challenge
When you go to buy the cubes for the rat run, you take the design to show the shopkeeper. They try to sell you more cubes than you need and insist they are included in the design.
Why? The perspective of the rat run design means there could be some blocks hidden behind others.
How many more cubes could they try to sell you?
I found another 6
What could you do to prove them wrong?
Draw a plan! (view from above) 1 4 2
This is the plan
of the rat run. The numbers tell you how many blocks high in each position. There are clearly 18in3 blocks.
This is the top view of the rat run with blocks added in places hidden behind existing blocks.
6 blocks have been
smuggled in (24in3)
but the original design
perspective would
not change. 1 4 2

15. Pet Accessory Plans and Elevations
Use the isometric drawings to match each pet accessory to the correct plan and front and side elevation.
Pet Accessory
Front elevation
Plan (top)
Right side elevation
Cat
Climb
Fish Feature
Rat Run
Challenge: Create a different possible plan for the rat run isometric drawing. How would this change the front and side elevations?

16. Pet Accessory Plans and Elevations Answers
Front elevation
Plan (top)
Right side elevation
Cat
Climb
Fish Feature
Rat Run

17. Create Your Own…
…perimeter, area and volume questions. Use the following templates to help you.

18. Garden Design
Key:
Shed
Flowerbed
Pond
Patio
Grass
1m2
Create your own perimeter and area questions based on your garden design.
Question cue ideas:
Calculate the perimeter of…
Calculate the area of…
Calculate the area of… and…
What fraction of the garden is used for…

19. Composite Shape Room Design
Create your own perimeter and area questions based on your design.
Question cue ideas:
Calculate the perimeter…
Calculate the area of…
What is the cost of…
What fraction of the area/perimeter is…
What percentage of the area/perimeter is…

20. Cake Design
Create your own circumference and area questions based on your design.
Question cue ideas:
Calculate the circumference of…
Calculate the area of…
What fraction of the area/circumference is…
What percentage of the area/circumference is…
What is the ratio of…

21. Pet Accessory Design
= 1…..3
Volume = …………3

22. Pet Accessory Plans and Elevations
front elevation
plan
side elevation