### Big ideas

Geometric figures have properties and relationships that allow us to calculate and analyse their sizes and dimensions.

### Chapter outline

### Idea summary

Techniques we can use to estimate area:

• Use a mental image of common objects of size 1 mm2, 1 cm2, 1 m2 and/or 1 km2 and try to picture how many it would take to cover the object.

• For shapes that are rectangular (or close to rectangular), estimate the length and width of the object and then multiply: Area = length × width.

• If a picture of the item is available, you could draw a scale grid over it and estimate by counting the number of squares needed to cover the item.

### Convert units of area

When we convert units of area we are changing the size of the squares that the area is measured in.

Interactive exploration

Explore online to answer the questions mathspace.co

Use the interactive exploration in 10.01 to answer these questions.

1. Check ‘Show Grid’ and cm2 to mm2. How many mm² in 1 cm2?

2. Check m2 to mm2. How many mm2 in 1 m2?

3. Check m2 to cm2. How many cm2 in 1 m2?

4. Check km2 to m2. How many m2 in 1 km2?

To convert units of area, such as from square centimetres (cm2) to square millimetres (mm2), consider the square with a side length of 1 cm. How many millimetres is each side length?

There are 10 mm in each 1 cm, so the square now becomes a square with side lengths of 10 mm each. Which has an area of 10 × 10 = 100 mm2?

When converting between units of area:

• Multiply if converting to a smaller unit — more smaller squares will be needed to cover the same area.

• Divide if converting to a larger unit — fewer larger squares will be needed to cover the same area.

### Example 5

Convert 6 m2 to cm2

Create a strategy

Sketch a square with side length of 1 m. We want to convert to centimetres, how many centimetres will each side length be and work out how many square centimetres is in 1 square metre.

Apply the idea

6 m2 = 6 × (100 × 100) Convert the square metre into centimetres = 60 000 cm2

Evaluate

### Idea summary

When converting between units of area:

• Multiply if converting to a smaller unit — more smaller squares will be needed to cover the same area.

• Divide if converting to a larger unit — fewer larger squares will be needed to cover the same area.

### Practice questions

Choose your question path

Explorer

1a-d, 2, 5–8, 10ab, 11, 12, 14–18

Adventurer

1e-h, 2, 3, 5–8, 10bc, 11–13, 15–21

Trailblazer

1i-l, 2–4, 6, 7, 9, 10cd, 11–13, 15–23

Understanding

1 From these units of measure,

• Hectares

• Square centimetres

• Square metres

• Square kilometres choose the most appropriate unit for these areas:

a Postage stamp b Bathroom wall c Paper d Cabinet

e City f Television g Kitchen h Farm

i Netball court j Table k National park l Door

2 Name an object that has an area of approximately 1 m2

3 Name an object that has an area of approximately 500 cm2.

*Ex 1, 2*

### Fluency

4 Find the area of a square of side 290 cm, in square metres.

5 Estimate the area of the Mathspace logo on the box.

6 This garden bed has three rows of four plants. Each plant is spaced about 24 cm apart, and sits 12 cm away from the edge of the garden bed.

Estimate the area of the garden bed in square centimetres.

7 Each square on the grid has an area of 4 mm2. Estimate the area of the curved shape.

8 Estimate the area of the shape shown if each axis is measured in metres.

9 Estimate the area of the butterﬂy if each axis is measured in millimetres.

10

Estimate the area:

a A 10 cm2

B 50 cm2

C 1 m2

D 100 mm2

c A 7000 cm2

B 6000 mm2

C 7 m2

D 400 mm2

11 Convert:

a 3 m2 to square centimetres

c 0.56 km2 to square metres

e 10.4 ha to square metres

g 3.5 m2 to square millilmetres

i 16.4 ha to square kilometres

k 0.38 km2 to hectares

### Reasoning

b A 200 cm2

B 55 000 mm2

C 6 m2

D 6000 cm2

d A 7000 mm2

B 2 m2

C 70 cm2

D 2000 mm2

b 7 m2 to square centimetres

d 6 ha to square metres

f 20 000 m2 to hectares

h 27.8 cm2 to square millilmetres

j 273 mm2 to square metres

l 0.101 km2 to square millimetres

12 There are 100 cm in 1 m but to convert from square metres to square centimetres we must multiply by 10 000. Explain why this is correct.

13 Determine whether these statements are true or false. Explain your reasoning.

a The unit of estimation must always be the same as the unit of measurement used to ﬁnd the exact area.

b The area of a square is equal to the perimeter of the square divided by 4.

c The area of a rectangle with length 5 cm and width 2 cm is equal to the area of a rectangle with length 2 cm and width 5 cm.

d The area of a shape can never be greater than its perimeter.

e When estimating area, it is always best to round the measurements to the nearest whole number.

14 Why is it a good idea to estimate the area of a shape before calculating it exactly?

15 A hectare is approximately the size of an athletics arena. Why are blocks of land, farms and large properties measured in hectares?