S1 Revision Notes on Area
What is area?
So area is measured in square units.
We can calculate the area by counting square units, for example:
b
In a) above the area is 6 square units
In b) the area is 8 square units
We can also find the area of irregular shapes like these ones:
In a) the area is 12 squares
In b) the area is 24 squares
So how do we calculate the area of a rectangle?
... and how do we find the area of a square?
A square is just a special rectangle which has equal sides.
If we call the sides L for length then we have a square like this:
L
Formula for area is:
L
Examples:
Area of a square = L x L
Areas of rectangles
a) Area = L x B
=4x8
= 32
b) Area = L x B
=7x9
= 63
Area of a square
c) Area = L x L
=6x6
= 36
Important note on units of area!!
Area can be measured in different units as follows:
1cm
or
1cm
is 1
1m
or
1m
is 1
1mm
1mm
is 1
(for very small areas)
or 1km
1 km
makes 1
(very large areas)
How do we calculate the area of a triangle?
Firstly let’s look at right angled triangles.
The area of a right angled triangle is half the area of the surrounding
rectangle.
This gives us the formula for the area of a right angled triangle with
base b and height h which is:
Area =
h
x base x height or A =
(alternative formula is A =
b
)
In fact this formula works for any triangle when you know the base and
the height, even triangles which don’t have a right angle so we have:
Here are some examples on triangle area:
1)
2)
A=
A=
=
=
= 7x2
=4x5
= 14
= 20
Area of compound shapes
You also need to know how to find the area of shapes which are made
up of two or more shapes joined together. These shapes are called
compound shapes or are sometimes called composite shapes.
You may have to find areas of composite shapes made of rectangles and
triangles. It’s easy to do this. You just split the shape up, find the
separate areas and add them together.
Examples:
a)
b)
2 rectangles:
c)
3 rectangles:
rectangle&triangle
Area 1 = 120
A 1 = 102
Area 2 = 72
A 2 = 84
Total area = 120+72
Total area = 102+84+72
= 192
Area rect = 238
A3 = 72
= 258
Area tri = 60
Total = 298
Important!! – it’s a good idea to sketch your composite shape and split it
into separate shapes – it makes it much easier to find the area!
Watch out when finding the area of compound shapes as you
sometimes have to find a missing length first!
For example:
5m
In this question if you split it
the way shown in the diagram
6m
Shape 1
xm
Shape 2
you need to find length x
2m
9m
Now we have: Area 1 = 30
Can you see that
x = 9 – 5 = 4m ?
Area 2 = 8
So total area = 30 + 8 = 38
Solving Word Problems
You also need to be able to solve word problems in context involving
area.
For example:
Frank is wallpapering a wall in his lounge.
The wall has the dimensions shown.
6m
3m
a) Calculate the area of the wall in
b) 1 roll of wallpaper will cover 4
of wall.
How many rolls will Frank need to buy to cover his wall. He can only buy
whole rolls.
c) How much wallpaper will he have left over?
d) If 1 roll of wallpaper costs £23.50, how much will Frank need to spend
on wallpaper?
Solution:
a) Area of wall = 3 x 6 = 18
b) 1 roll covers 4
so Frank will need 5 rolls to cover the 18
5 x 4 = 20
c) He will have 2
left over since 20 – 18 = 2
d) He uses 5 rolls so it will cost him 5 x £23.50 = £117.50
S1 Revision Questions on Area
Please attempt the questions below at the appropriate level:
2nd Level Questions
Calculate the area of these shapes by counting the centimetre squares.
In Q3:
if more than half a box covered count it as 1
if less than half a box covered don't count it at all
1.
4.
2.
3.
Calculate the area of these squares and rectangles using the formulae:
Area of a rectangle = L x B
Area of a square = L x L
Remember to use the correct units of area
a)
6cm
b)
3cm
5.
28cm
c)
4cm
7m
Calculate the area of these right angled triangles using the formula
Area =
bxh
a)
or
Area =
b)
10cm
5cm
6cm
8cm
7m
6. Natalia is painting a wall in her bedroom.
The wall has the dimensions shown.
5m
4m
a) Calculate the area of the wall in
b) 1 litre tin of paint covers 3
.
How many litre tins will Natalia need to buy to paint her wall?
c) If 1 litre tin costs £13.50, how much will Natalia need to spend on paint?
3rd Level Questions
1.
Calculate the area of these squares and rectangles using the formulae:
Area of a rectangle = L x B
Area of a square = L x L
Remember to use the correct units of area
a)
9cm
b)
7cm
2.
13.3cm
6cm
9m
9m
Calculate the area of these triangles using the formulae
Area =
bxh
or
Area =
a)
b)
6.5cm
3.
c)
10.4cm
12.5m
8cm
6m
Calculate the missing dimension
in these shapes with the given area
(a)
9m
xm
Rectangle: area = 45
(b)
x cm
x cm
Square: area = 36
4. Amrit is varnishing the floor in the lounge.
5m
The floor has the dimensions shown.
5.5m
a) Calculate the area of the floor in
b) 1 litre tin of varnish covers 4
How many litre tins will Amrit need to varnish the floor?
c) If 1 litre tin costs £13.25, how much will she need to spend on varnish?
5. Find the total area of these shapes by splitting them into two or more rectangles and
then adding the separate areas.
Calculate the missing dimension first when required.
(a)
(c)
(b)
? cm
(d)
6. Melissa is tiling the floor of her kitchen and bathroom and the plan is shown in the
diagram below.
8m
5m
kitchen
bathroom
1.5m
12m
(a) Calculate the total area of floor which Melissa has to tile.
(b) Each box of tiles contains enough tiles to cover 8
need to buy?
. How many boxes does Karolina
(c) If one box of tiles costs £42, how much will Karolina spend on tiles?
4th Level Questions
1.
Calculate the area of these squares and rectangles using the formulae:
Area of a rectangle = L x B
Area of a square = L x L
Remember to use the correct units of area
a)
16cm
b)
9cm
2.
4.65m
9m
c)
17m
17m
Calculate the area of these triangles using the formulae:
Area =
bxh
or
Area =
a)
b)
27mm
16mm
5.4m
8m
3.
Calculate the missing dimension
(a)
17m
in these shapes with the given area
(b)
x cm
xm
x cm
Rectangle: area = 51
Square: area = 144
4. Alistair works in Princes Street Gardens and is sowing grass seed on a lawn in the shape
of a right angled triangle.
The lawn has the dimensions shown.
(a) Calculate the area of the lawn.
7.4m
(b) He needs 1 kg of grass seed to sow every 4 square
metres of grass. How many 1 kg bags of seed will he
need to buy to sow the entire lawn?
8m
(c) If seed costs £9.95 per kg, how much will it cost to
buy the required amount of grass seed?
5. Find the area of these compound shapes, giving you answer using the appropriate
units. Find the missing sides first if necessary.
(a)
8.5 cm
7cm
(b)
6cm
12cm
12.5m
7m
16m
6. A local council is building a playpark for children and the plan is shown below.
The playpark is made up of a rectangular section and a triangular section.
5.5m
10.5m
7m
(a) Calculate the total area of the playpark.
(b) Rubber surfacing for the playpark costs £19 per square metre.
How much will the council need to pay to surface the entire playpark?
(c) Round the answer in (b) to the nearest £10.
Answers to revision questions are on website!