MEP Practice Book ES
Facts to Remember
Unit 7
x
Square: Area = x 2
x
x
x
w
w
Rectangle: Area = lw
ll
Triangle: Area =
1
bh
2
a
c
hh
bb
Circle: Area = π r 2
r
Parallelogram: Area = bh
h
Circumference = 2 π r
h
b
b
a
a
1
Trapezium: Area = ( a + b )h
2
h
h
b
b
a
a
1
Kite: Area = ab
2
b
b
a
Cube: Volume = a 3
a
a
b
Cuboid: Volume = abc
Surface area = 6 a 2
Surface area = 2( ab + bc + ca)
c
a
h
2
Cylinder: Volume = π r h
Surface area = 2π r 2 + 2π rh
r
l
Prism: Volume = Al
h
A
b
Pyramid: Volume =
1
Ah
3
1
Cone: Volume = πr 2 h
3
h
A
hh
rr
Sphere: Volume =
Anwar Sir, O/A level Mathematics Teacher
4 3
πr
3
r
r
Surface area = 4 π r 2
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BACKGROUND KNOWLEDGE AND GEOMETRIC FACTS/ANH
4
For some shapes we can derive a formula for perimeter. The formulae
for the most common shapes are given below:
b
a
w
l
r
r
d
q°
c
l
square
rectangle
triangle
circle
P = 4l
P = 2(l + w)
P = a+ b+ c
C =2¼r
or C = ¼d
arc
µ
l = ( 360
)2¼r
The length of
an arc is a
fraction of the
circumference
of a circle.
AREA FORMULAE
Shape
Figure
Rectangle
Formula
Area = length £ width
width
length
Triangle
Area = 12 base £ height
height
base
base
Parallelogram
Area = base £ height
height
base
a
Area =
Trapezium
or
Trapezoid
h
(a +2 b) £h
b
Circle
Area = ¼r2
r
Sector
Area =
q
µ
(360
) £¼r
2
r
SURFACE AREA FORMULAE
RECTANGULAR PRISM
c
a
Anwar Sir, O/A level Mathematics Teacher
Cell: 01712531475, 01972531475
100
95
75
50
25
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Fri Jun 25 11:08:39 2004
0
100
95
75
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cyan
A = 2(ab + bc + ac)
b
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16
BACKGROUND KNOWLEDGE AND GEOMETRIC FACTS
CYLINDER
CONE
Object
Outer surface area
Object
Outer surface area
Hollow cylinder
A = 2¼rh
(no ends)
Open cone
A = ¼rs
(no base)
hollow
r
h
s
r
hollow
A = 2¼rh + ¼r2
(one end)
Open can
hollow
Solid cone
r
h
r
A = ¼rs + ¼r2
(solid)
s
solid
A = 2¼rh + 2¼r2
(two ends)
Solid cylinder
solid
SPHERE
h
r
r
solid
Area,
A = 4¼r2
VOLUME FORMULAE
Object
Figure
Solids of
uniform
cross-section
Volume
Volume of uniform solid
= area of end £ length
height
end
height
end
height
height
Pyramids
and
cones
h
base
base
r
Volume of a sphere
= 43 ¼r3
Spheres
Anwar Sir, O/A level Mathematics Teacher
Cell: 01712531475, 01972531475
100
95
75
50
25
5
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Fri Jun 25 11:08:48 2004
0
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95
75
50
25
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Volume of a pyramid
or cone
= 13 (area of base £ height)
black
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