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Middle Years

10.03 Area of rectangles and squares

Worksheet
Area of a rectangle
1

In the following diagrams, each grid square represents 1 square unit. Find the area of the following shapes by counting the number of grid squares it covers:

a
b
2

The area of the shape shown was measured using a centimetre grid.

What unit should we use to describe its area?

3

For each of the following pairs of shapes:

i

Find the area of Shape A.

ii

Find the area of Shape B.

iii

State which shape is the smallest.

a
b
4

For each of the following pairs of shapes:

i

Find the area of Shape A.

ii

Find the area of Shape B.

iii

State which shape is the largest.

a
b
c
d
e
f
5

Order the three shapes from smallest to largest.

6

Consider the two overlapping squares shown:

State which square is the largest.

7

For each of the following:

i

Find the length and width of the rectangle.

ii

Find the area of the rectangle.

a
b
c
d
Area from dimensions
8

Find the area of the following rectangles:

a
b
c
d
e
f
9

Find the area of the following squares:

a
b
c
10

Find the area of the following:

a

A square whose side is 7\text{ cm}.

b

A rectangle whose length is 7 \text{ cm} and width is 3\text{ cm}.

c

A rectangle whose length is 12\text{ cm} and width is 5\text{ cm}.

11

A square has a perimeter of 32\text{ cm}.

a

Find the side length of the square.

b

Find the area of the square.

12

For each of the following rectangles:

i

Find the perimeter.

ii

Find the area.

a
b
c
d
Dimensions from area
13

Find the length of the missing side in the following rectangles:

a
b
14

Find the side length of the following square:

15

Find the length of the missing side in the following rectangles:

a

A rectangle that has an area of 36\text{ m}^2 and a width of 4\text{ m}.

b

A rectangle that has an area of 18\text{ m}^2 and a length of 9\text{ m}.

Applications
16

The given table shows the areas of some Asian countries:

a

Which country is smaller in area than Malaysia?

b

Which country is nearly four times the size of Thailand?

c

Which country is larger than Japan but smaller than Indonesia?

\text{Country}\text{Area (km}^2\text{)}
\text{Thailand}514\,000
\text{Japan}377\,835
\text{Indonesia}1\,904\,569
\text{Malaysia}329\,750
\text{Sri Lanka}65\,610
17

The given table shows the areas of the Australian states:

a

Which state is the largest?

b

Which state is the smallest?

c

Which state is about the same size as New South Wales and South Australia combined?

d

Which state is about a quarter of the size of South Australia?

\text{State}\text{Area (km}^2)
\text{Western Australia}2\,529\,875
\text{New South Wales}800\,642
\text{Queensland}1\,730\,648
\text{Tasmania}68\,102
\text{Victoria}227\,416
\text{South Australia}983\,482
18

A rectangular driveway is 5\text{ m} long and 3\text{ m} wide. Find the area of the driveway.

19

A basketball court is 29\text{ m} long and 15\text{ m} wide. Find the area of the basketball court.

20

A rugby field is 100\text{ m} long and 70\text{ m} wide. Find the area of the rugby field.

21

A rectangular park has an area of 40\text{ m}^2. If the park is 5\text{ m} wide, find its length.

22

Homer's dining table is 7\text{ m}^2. He buys a tablecloth that covers a rectangular area that is 1.9\text{ m} wide and 3\text{ m} long.

a

Find the area of the tablecloth.

b

The tablecloth is too small, how much larger does the tablecloth need to be to cover Homer’s table?

23

Gwen is digging a rectangular garden bed to plant some new hedging.

a

If the garden bed is 0.5\text{ m} wide and 6\text{ m} long, find the total area of the garden bed.

b

Each hedge plant fills an area that is the same as 1 square metre. How many hedge plants are needed to fill Gwen’s garden bed?

24

A kitchen floor is tiled with the tiles shown in the picture. If 50 tiles are needed to tile the floor, find the total area of the floor.

25

Dave made a square mosaic that has a side length of 2\text{ m}. Dave decided to add a border to his mosaic, and now it has a side length of 2.3\text{ m}. By how much has the area of the mosaic increased?

26

A farmer wants to cover a rectangular section of roofing that measures 6\dfrac {1}{2} \text{ m} by 9\dfrac {1}{2} \text{ m} with solar panels. Having received quotes from various solar panel suppliers, she estimates that the panels will cost \$300 per square metre to install. Calculate the estimated cost of covering the section of roofing with solar panels.

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