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4.03 Units of area

Worksheet
Units of area
1

Consider the following units of measure for area:

  • Hectares

  • Square centimetres

  • Square metres

  • Square kilometres

Choose the most appropriate unit of measure for the following areas:

a

Postage stamp

b

Bathroom wall

c

Australia

d

Matchbox

e

Exercise book

f

Street

g

School playground

h

Pencil case

i

Japan

j

Cabinet

k

City

l

Television

m

Kitchen

n

Farm

o

Classroom

p

Netball court

q

Table

r

National park

s

Door

2

Convert the following to the unit indicated:

a

3\text{ m}^{2} to square centimetres

b

7\text{ m}^{2} to square centimetres

c

0.56 \text{ km}^{2} to square metres

d

810 \text{ mm}^{2} to square centimetres

e

34\,000 \text{ mm}^{2} to square metres

f

790\,000\,000\text{ cm}^{2} to square kilometres

g

6 \text{ ha} to square metres

h

10.4 \text{ ha} to square metres

i

20\,000 \text{ m}^{2} to hectares

j

54\,800 \text{ m}^{2} to hectares

3

Find the area of a square of side 290 \text{ cm}, in square metres.

Estimating area
4

Estimate the total area of the artwork above the sofa, in square centimetres, if the sofa is 1.9 \text{ m} in length.

5

The following garden bed has three rows of four plants. Each plant is spaced about 24 \text{ cm} apart, and sit 12 \text{ cm} away from the edge of the garden bed:

Estimate the area of the garden bed in square centimetres.

6

Each square on the grid has an area of 9 \text{ mm}^{2} . Estimate for the area of the curved shape shown:

7

Each square on the grid has an area of 4 \text{ mm}^{2}. Estimate the area of the curved shape shown:

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

These road signs are pictured with relative sizings. If the GIVE WAY sign is an equilateral triangle with a side length of 75 \text{ cm}, estimate the area of the BICYCLES EXCEPTED sign.

11

Estimate the areas of the following shapes:

a
b
c
d
12

Name an object that has an area of approximately 1 \text{ m}^{2}.

13

Name an object that has an area of approximately 500\text{ cm}^{2}.

Applications
14

A park has an area measuring 19 acres. Given that 1 acre is approximately 4000 \text{ m}^2, find the area of the park in square metres.

15

Rectangular farms around Australia were measured and their dimensions, in metres, are recorded in the following table:

a

Find the area of each farm in square metres.

b

Which farms have an area of more than 1 \text{ ha}?

c

Which farms have an area of less than 1 \text{ ha}?

d

Which farm has an area of exactly 1 \text{ ha}?

\text{Farm}\text{Length, m}\text{Width, m}\text{Area, m}^2
1200100
235021
310024
440040
5100100
16

A property covers an area of 4.5 \text{ ha}. Given that 1 \text{ ha} is 10\,000 \text{ m}^2, calculate the following:

a

The area of the property in square metres.

b

The area of the property in acres, given that 1 acre is approximately 4000 \text{ m}^2.

17

A large cattle station covers an area of 320 acres. Given that 1 acre is approximately 0.4 \text{ ha}, and 1 \text{ ha} is 10\,000 \text{ m}^2, calculate the following:

a

The area of the cattle station in hectares.

b

The area of the cattle station in square kilometres.

18

A farm covers an area of 51\,000 \text{ m}^2. Given that 1 \text{ ha} is 10\,000 \text{ m}^2, and 1 acre is approximately 4000 \text{ m}^2, calculate the following:

a

The area of the farm in hectares.

b

The area of the farm in acres. Round your answer to two decimal places.

19

Bob owns a paddock with an area of 290 acres. He wants to advertise his eggs as free range, with no more than 400 chickens per hectare. Given that 1 acre is approximately 0.4 \text{ ha}, find the largest amount of chickens that Bob can keep in his paddock.

20

A farm covers an area measuring 340 acres. Given that 1 acre is approximately 0.4 \text{ ha}, and 1 \text{ ha} is 10\,000 \text{ m}^2, calculate the following:

a

The area of the farm in hectares.

b

The area of the farm in square metres.

21

American football is played on a field with an area of 12\,000 \text{ yd}^2.

a

Given that 1 \text{ yd}^2 is approximately 0.836\text{ m}^2, find the area of an American football field in square metres.

b

The MCG oval has an area of 17\,700\text{ m}^2. How much smaller than the MCG oval is an American football field? Give your answer in square metres.

22

Manhattan, the most densely populated borough of New York City, has an area of 22.8\text{ mi}^2. If 1\text{ mi}^2 is approximately 2.6 \text{ km}^2, how large is Manhattan in square kilometres?

23

The state of California is roughly 164\,000 \text { mi}^2 in area. Given that 1 \text { mi}^2 is approximately 2.6 \text{ km}^2:

a

Find the area of California in square kilometres.

b

The state of New South Wales has an area of approximately 809\,000 \text{ km}^2. How much larger is New South Wales than California?

24

An official NBA court covers 4700 \text{ ft}^2 in area. Given that 1 \text{ m}^2 is approximately 10.8 \text{ ft}^2, find the area of an official basketball court in square metres. Round your answer to three decimal places.

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Outcomes

1.3.5

choose and use appropriate metric units of area, their abbreviations and conversions between them

1.3.6

estimate the areas of different shapes

1.3.7

convert between metric units of area and other area units

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