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KS3 Mathematics
S8 Perimeter, area and volume
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Contents
S8 Perimeter, area and volume
S8.1 Perimeter
S8.6 Area of a circle
S8.2 Area
S8.5 Circumference of a circle
S8.3 Surface area
S8.4 Volume
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Put these shapes in order
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Perimeter
To find the perimeter of a shape we add together the length of all the sides.
What is the perimeter of this shape?
1 cm
3
3
2
11
2
Perimeter = 3 + 3 + 2 + 1 + 1 + 2
= 12 cm
Starting point
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Perimeter of a rectangle
To calculate the perimeter of a rectangle we can use a formula.
length, l
width, w
Using l for length and w for width,
Perimeter of a rectangle = l + w + l + w
= 2l + 2wor
= 2(l + w)
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Perimeter
What is the perimeter of this shape?
b cm
a cm
9 cm
5 cm
12 cm 4 cm
The lengths of two of the sides are not given so we have to work them out before we can find the perimeter.
Let’s call the lengths a and b.
Sometimes we are not given the lengths of all the sides. We have to work them out using the information we are given. For example,
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Perimeter
9 cm
5 cm
b cm
12 cm
a cm
4 cm
a = 12 – 5 cm
= 7 cm
7 cm
b = 9 – 4 cm
= 5 cm
5 cm
P = 9 + 5 + 4 + 7 + 5 + 12
= 42 cm
Sometime we are not given the lengths of all the sides. We have to work them out from the information we are given.
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Calculate the lengths of the missing sides to find the perimeter.
P = 5 + 2 + 1.5 + 6 + 4 + 2 + 10 + 2 + 4 + 6 + 1.5 + 2
Perimeter
5 cm
2 cm
6 cm
4 cm4 cm
2 cm2 cm
p
q r
s
t
u
p = 2 cm
q = r = 1.5 cm
s = 6 cm
t = 2 cm
u =10 cm
= 46 cm
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P = 5 + 4 + 4 + 5 + 4 + 4
Perimeter
What is the perimeter of this shape?
Remember, the dashes indicate the sides that are the same length.
5 cm
4 cm
= 26 cm
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Perimeter
Perimeter = 4.5 + 2 + 1 + 2 + 1 + 2 + 4.5
Start by finding the lengths of all the sides.
5 m
2 m
2 m
2 m
4 m
4.5 m 4.5 cm
1 cm1 cm
= 17 cm
What is the perimeter of this shape?
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Before we can find the perimeter we must convert all the lengths to the same units.
Perimeter
3 m
2.4 m
1.9 m
256 cm
In this example, we can either use metres or centimetres.
Using centimetres,
300 cm
240 cm
190 cm
P = 256 + 190 + 240 + 300
= 986 cm
What is the perimeter of this shape?
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Equal perimeters
Which shape has a different perimeter from the first shape?
A B C
A B C
A B C
B
A
A
