Perimeter/Area
Perimeter/Area of a Square, Rectangle, Triangle
Be able to use
formulae to find
perimeter/area of
a square,
rectangle, triangle
Revision
Examples :- Calculate the perimeter and area of each of these shapes :-
5 cm
square
3 cm
5 cm
8 cm
rectangle
triangle
8 cm
Perimeter = 5 + 5 + 5 + 5
10 cm
Perimeter = 10 + 8 + 6
Perimeter = 3 + 8 + 3 + 8
= 25 cm
= 22 cm
Area = L x L
Area = L x B
= 5 x 5
= 25 cm
6 cm
4·8 cm
= 24 cm
Area =
= 3 x 8
2
= 0·5 x 10 x 4·8
= 24 cm 2
= 24 cm 2
=> Area is in cm2
If the length and breadth are in cm
1
x B x H
2
* the area of a triangle can also be calculated
by finding half the surrounding rectangle
If the length and breadth are in mm => Area is in mm2
=> Area is in m2
If the length and breadth are in m
Exercise 1
1. Calculate :-
(i) the perimeter
a
(ii) the area of each of these shapes :-
b
c
5·5 cm
10 cm
square
9 cm
8 cm
4 cm
d
17 cm
e
15 cm
8 cm
6 cm
17 cm
1·5 cm
g
h
15 cm
9 cm
3·5 cm
this is page 67
10 cm
i
square
12 cm
12 cm
CfE Book 3a - Chapter 8
12·5 cm
f
0·5 cm
Perimeter/Area
2.
Calculate the areas of the objects shown below,
using an appropriate formula :a
Kiltie Photo
b
Sponge Bob’s
Square Head
side 9 cm
200 mm
120 mm
Union
Jack
c
30 m
d
7-a-side
football
pitch
2m
18 m
2·5 m
e
f
triangular
mayo
sandwich
yacht’s
blue sail
4m
14·5 cm
find the
area of this
face.
3.
1·2 m
10 cm
Donnie decides to varnish his Youth Club Hall floor.
a
Calculate the area of the floor.
b
A litre of varnish covers 17 m2 .
8·5 m
How many litres will be needed for one coat of varnish ?
c
If a litre tin costs £6·50, what will it cost to cover the floor with two coats of varnish ?
4.
The diagram shows the carpeted floor of Mandy’s bedroom.
2·7 m
4·7 m
5.
20 m
a
Calculate the perimeter of the floor.
b
How much will it cost to surround it with
new skirting board costing £2·50 per metre ?
(The door is 0·80 metre wide).
Farmer McDougall owns a rectangular field.
He surrounds it with 3 strands of barbed wire.
The wire costs 80p per metre.
Calculate the total cost of the wire.
CfE Book 3a - Chapter 8
55 m
this is page 68
70 m
Perimeter/Area
Be able to use
formulae to find
the area of a
rhombus & a kite
The Area of a Rhombus and a Kite
Area of a Rhombus
Area of a Kite
Draw (or imagine) the rectangle that neatly
surrounds the rhombus.
Found in the same way as
the Rhombus.
5 cm
8 cm
16 cm
12 cm
The rhombus shown above has length 16 cm
and height 5 cm.
Area Rect. = L x B = 12 x 8 = 96 cm2 .
Area Kite =
Its Area is calculated by finding the area of
the surrounding rectangle and then halving
the answer found.
Area Rhombus =
Area Kite =
1
2
diagonal x diagonal
=
1
2
x
of 80 cm = 40 cm .
2
2
or
Area =
1
2
diagonal x diagonal
1
2
(D x d)
12 x 8
= 48 cm2 .
Note that the length and breadth of a rhombus
are actually the measurements of its diagonals.
Area of Rhombus =
of 96 cm2 = 48 cm2 .
OR
Area Rect. = L x B = 16 x 5 = 80 cm2 .
1
2
1
2
Area of Kite =
or
(where D and d are lengths of big and small diagonals).
1
2
Area =
diagonal x diagonal
1
2
(D x d)
(where D and d are lengths of big and small diagonals).
Exercise 2
1.
2.
a
Make an accurate drawing of a rhombus with diagonals measuring 6 cm by 8 cm.
(Draw the 2 diagonals 6 cm by 8 cm meeting at right angles in the middle.)
b
On your diagram, draw a rectangle neatly around the rhombus.
c
Calculate the area of the rectangle.
d
Now calculate the area of the rhombus.
Sketch each rhombus below and surround it with a rectangle.
a
Calculate the area of the rectangle.
(i)
15 cm
8 cm
CfE Book 3a - Chapter 8
b
Calculate the area of the rhombus.
(ii)
(iii)
5 cm
this is page 69
12 cm
20 cm
6·5 cm
Perimeter/Area
3.
Use the formula “Area of Rhombus =
a
1
2
(D x d)” to find the areas of these rhombi :-
b
10 cm
c
20 cm
6 cm
12 cm
8 cm
3·5 cm
2·6 cm
40 mm
d
e
f
2m
55 mm
7·4 cm
6·2 m
4.
Use the formula “Area of Kite =
3 cm
a
1
2
(D x d)” to find the areas of these kites :b
9 cm
2 cm
c
7 cm
9·5 cm
12 cm
d
e
f
35 m
5·2 cm
10 cm
80 mm
50 m
120 mm
3·2 m
5.
“Kites - 4 - All” fly a giant kite above their new store in Hillington.
Kites-4-All
The kite is strengthened by 2 plastic poles measuring 3·2 metres
and 4 metres which are fitted as diagonals of the feature.
4·0 m
Calculate the area of their giant kite.
6.
Local fishermen used to nickname this fish “The Rhombus”.
Find the approximate area of its body if its measurements
are 30 cm long and 12 cm in height.
7.
The base of this trowel is in the shape of a kite.
Find its area of its top surface.
18 cm
12·5 cm
CfE Book 3a - Chapter 8
this is page 70
Perimeter/Area
8.
Simon bought a pair of cufflinks, each one
in the shape of a rhombus.
The diagonals of each rhombus are 0·9 centimetres
and 1·4 centimetres.
Calculate the total area taken up by the 2 faces of rhombi.
9.
Debbie’s necklace is made up of 3 identical golden rhombi on a chain.
1·5 cm
6·9 cm
The 3 rhombi together measure 6·9 centimetres long and each has a height of 1·5 centimetres.
Calculate :a
the length of the diagonal of one of the rhombi.
b
the total area of the 3 golden rhombi.
10. Calculate the area of the star-shape,
constructed from 4 identical kites.
7 cm
20 cm
11. Calculate the area of each V-kite.
a
b
c
160 mm
16 m
8m
22 m
15 cm
60 mm
90 mm
20 cm
B
12. The area of rhombus ABCD is 150 cm2.
The length of diagonal AC is 30 cm.
A
Area = 150 cm2
C
Work out the length of diagonal BD.
D
CfE Book 3a - Chapter 8
this is page 71
Perimeter/Area
Be able to use
formulae to find
the area of a
parallelogram
The Area of a Parallelogram
It should be easy to see why .........
the area of a parallelogram
Remember :-
=
the area of a rectangle.
Example :-
(Area of Rectangle = Length x Breadth)
2 cm
4·5 cm
A difference in notation :-
Area = B(ase) x H(eight)
AREA of Parallelogram = Base x Height
= 4·5 x 2
= 9 cm2
Exercise 3
1.
This is a sketch of a parallelogram.
8 cm
Use the formula Area = B x H to find its area.
2.
20 cm
Calculate the area of each parallelogram :a
b
c
9 cm
5 cm
13 cm
11 cm
d
4 cm
18 cm
e
f
11 cm
12 cm
2 cm
4·5 cm
g
4 cm
h
9·2 cm
12·5 cm
i
13·8 cm
18 cm
3·6 cm
15 cm
4 cm
11 cm
CfE Book 3a - Chapter 8
1·75 cm
this is page 72
Perimeter/Area
3.
This light switch is in the shape of a parallelogram.
65 mm
Calculate its area.
62 mm
90 mm
4.
Mr Ainslie has a lawn in the shape of a parallelogram.
Calculate the area of his lawn.
5·2 m
20 m
5.
The ramp in this garage is the shape of a parallelogram.
2·4 m
Calculate the area of the gap shown.
6m
6.
4 Mechano Strips are joined to make a parallelogram shape.
Calculate the area of the shape formed.
20 cm
60 cm
7.
A sloping wooden plank is used to help
strengthen 2 upright posts.
5 cm
48 cm
8.
Calculate the area of the sloping plank.
Movable stairways are used on the London Tube to
take passengers from below ground up to street level.
Again, parallelogram shapes are noticeable.
Find the area of the large parallelogram.
9.
U
T
S
Q
21 cm
12·4 m
1·4 m
Look at the diagram opposite.
18 cm
P
1·2 m
R
a
Use four letters each time
to name 2 parallelograms.
b
Calculate the area of each
parallelogram.
45 cm
10. The area of this parallelogram is 375 mm2 .
? mm
Calculate its height.
25 mm
CfE Book 3a - Chapter 8
this is page 73
Perimeter/Area
Be able to find
the area of a
trapezium by
making 2 triangles
The Area of a Trapezium
A Trapezium is a 4-sided figure (Quadrilateral) with 2 sides parallel.
The Area of a Trapezium is found by :• drawing in one of its diagonal lines, splitting the figure into 2 triangles,
• working out the area of each triangle,
• adding the 2 triangular areas together.
3 cm
Example :-
A TRAPEZIUM
A
8 cm
B
Area ! A =
1
x
2
B x H =
1
x
2
3 x 8
=
12 cm2
Area ! B
1
x
2
B x H =
1
x
2
18 x 8 =
72 cm2
= 12 cm2 + 72 cm2 =
84 cm2
=
Total Area
18 cm
Exercise 4
1.
For each of the following, sketch and split each trapezium into 2 triangles and find its area :a
3 cm
b
6 cm
7 cm
16 cm
6 cm
9 cm
20 cm
10 cm
6 cm
9·5 cm
d
c
e
f
68 mm
28 mm
80 mm
8 cm
50 mm
60 mm
40 mm
1·5 cm
2.
3·5 cm
2 cm
Calculate the area of this Malaysian stamp.
1·8 m
4 cm
3.
The top of this table in the school library is a trapezium.
Find its area in cm2 .
4.
10 cm
96 cm
1·4 m
Joe has alloy wheels on his car.
Each gap is trapezium shaped.
20 cm
Calculate the total area taken up
by the 6 gaps in one wheel.
18·4 cm
CfE Book 3a - Chapter 8
this is page 74
Perimeter/Area
Be able to
calculate the area of
a figure made up of
2 or more shapes
Composite Areas
We now look at examples which combine the areas
which we have studied in this chapter.
Example :Calculate the area of this composite shape consisting
of a triangle with a square along one side.
7 cm
Area Square = L x L
Area Triangle =
1
2
B xH
= 7x7
=
1
2
of 10 x 5·2
= 49 cm2
= 26 cm2
8 cm
5·2 cm
10 cm
TOTAL = 75 cm2
Exercise 5
1.
Calculate the shaded areas :a
Rectangle with
Square removed
b
Square &
Triangle
Rectangle with
Rhombus removed
c
16 cm
15 cm
12 cm
9 cm
8 cm
30 cm
27 cm
d
12 cm
Parallelogram with 2
Identical Kites removed
Trapezium with
Triangle removed
e
f
Triangle and Two
Identical Parallelograms
200 mm
100 mm
40 m
14 m
144 mm
60 m
70 cm
20 cm
36 mm
10 cm
10 m
2.
Find the area of this house shape.
9m
6·5 m
The house is rectangular and has
a “trapezium” roof.
18 m
CfE Book 3a - Chapter 8
this is page 75
Perimeter/Area
3.
Calculate these areas :a
b
10 cm
0·8 cm
c
9 cm
8 cm
9 cm
9 cm
12 cm
6 cm
2 cm
5 cm
0·8 cm
5 cm
16 cm
d
e
5 cm
f
3·5 m
3 cm
10 cm
3·5 m
16 cm
10 cm
3 cm
4·5 cm
18 cm
4.
1·5 m
Calculate the area of this arrow head, consisting
of a triangle and a rectangle :18 cm
1·5 cm
6 cm
32 cm
5.
4·6 m
Calculate the wooden area of the side of this hut.
1·6 m
The dimensions of the window are 0·5 m by 1·6 m.
0·5 m
3·2 m
3m
6.
Calculate the area of these composite shapes :a
b
13 m
80 m
28 m
8m
4m
16 m
60 m
50 m
14 m
30 m
90 m
8m
CfE Book 3a - Chapter 8
this is page 76
Perimeter/Area