1. Find the area of each of the following figures.
6 cm
(a)
9 cm
(b)
(c)
2 cm
5 cm
Rectangle
6 cm
Triangle
Square
13 cm
(d)
(e)
10 cm
(f)
69 cm
10 cm
29 cm
8 cm
13 cm
12 cm
20 cm
52 cm
Parallelogram
Triangle
15 cm
Trapezium
2. Each of the following figures is formed by rectangles. Find the area of the shaded region in each of
the following figures.
(a)
8 cm
A
2 cm
F
10 cm
(b)
H
4 cm
A
6 cm G
3 cm
6 cm D
E
L
(d)
7 cm
A
D
J
B
C
3 cm
12 cm
5 cm
C
(e)
D
6m
12 cm
6m
H
E
B
7 cm
2m
3m
F
(f)
10 cm
A
D
E
C
F
W
C
I
G
8 cm
X
8 cm
G
C
6m
12 cm
12 cm
J
F 3m G
D
25 cm
A
32 cm Z
B
C
20 cm
E 4 cm H
F
E
F
Y
6 cm
H
10 m
A
2m
B
K
5 cm
8 cm
I
(c)
4 cm
D
B
4 cm
H
Y 1 cm
X
2 cm 8 cm
Z
W
4 cm
E
B
G
2 cm
10.35
 2009 Chung Tai Educational Press. All rights reserved.
3. Find the area of the shaded region in each of the following figures.
A 3.5 cm J
(a)
H
I
B
(c)
C
2 cm
G
B
A
(b)
1.5 cm
8 cm
E
9 cm
2 cm
F
E
16 cm
C
C 3.5 cm D
E
10 cm
B
12 cm
5 cm
3 cm
D
G 5 cm A
6 cm
1.5 cm
F
12 cm
D
4. Find the area of the shaded region in each of the following figures.
(a)
A
8 cm
A
(b)
B
(c)
B
8 cm
C
5 cm
E
F 4 cm G
25 cm
12 cm
12 cm
D
F
18 cm
B
E
E
20 cm
C
13 cm
15 cm
6 cm
A
CG
8 cm
H
D
12 cm
D
24 cm
5. Find the area of the shaded region in each of the following figures.
A
(a)
20 cm
D
(b)
A
15 cm
I
D
20 cm
(c)
E
A
B
20 cm
E
F
30 cm
40 cm
F
H
16 cm
18 cm
10 cm
B
C
D
C
50 cm
G
BE and CD meet at F.
G
B
C G
F
14 cm
AF and CD meet at H.
10.36
 2009 Chung Tai Educational Press. All rights reserved.
E
AD and CE meet at F.
6. In the figure, if the area of the shaded region is 31 cm2 , find the
value of x.
A
x cm
C
3 cm
2 cm
G
B
P 2 cm D
F
2 cm
E 2 cm Q
10 cm
7. In the figure, ABCD is a parallelogram. E is a point on BC
such that DE  BC . BF  CF, AB  15 cm , BF  7 cm and
CF  24 cm .
D
C
E
24 cm
(a) Find the area of ABCD.
(b) Find the length of BC.
(c) Find the length of DE.
A
15 cm
B 7 cm F
S
8. The figure shows quadrilateral PQRS. If M and N are points on QR
such that PM  6 cm, SN  10 cm , QN  11 cm and RM  14 cm ,
find the area of quadrilateral PQRS.
P
[ Hint: Let MN  x cm. ]
Q
M
N
R
9. Find the unknown in each of the following pairs of similar figures.
(a)
3.2 cm
(b)
2 cm
12 cm
4 cm
Area  18 cm2
Area  x cm2
Area  2 cm2
Area  y cm2
10.37
 2009 Chung Tai Educational Press. All rights reserved.
10. Find the unknown in each of the following pairs of similar figures.
x cm
(a)
(b)
1.2 cm
7.5 cm
y cm
Area  4 cm
2
Area  9 cm
Area  50 cm2
Area  18 cm2
2
B
11. In the figure, ABCD and AFGE are two similar figures. If the
C
4 cm
area of AFGE is 56 cm2, find the area of ABCD.
G
F
8 cm
A
12. In the figure, ABCDEF and APQRST are two similar figures,
2
E
D
C
2
their respective areas are 125 cm and 20 cm . Find the length
of PB.
R
Q
6 cm
A
P
T
S
E
F
figures, their total area is 111.25 cm2 . Let x cm2 be the area of
IJKLMNOP.
B
C
(a) Express the area of ABCDEFGH in terms of x.
A
P
(b) Find the area of ABCDEFGH and the area of IJKLMNOP.
E
N
K
M
L
O
3 cm
 2009 Chung Tai Educational Press. All rights reserved.
B
D
13. In the figure, ABCDEFGH and IJKLMNOP are two similar
10.38
D
F
G
I
H
J
10 cm
3 cm
14. In the figure, ABC ~ ADE . The area of the shaded region a nd
the area of ABC are 64 cm2 and 36 cm2 respectively.
A
(a) Find the ratio of the area of ABC to that of ADE.
(b) Find the length of AB.
B
C
6 cm
D
E
15. Two pieces of iron wire of different lengths are bent into two
similar polygons in the star shape, where the ratio of the
lengths of the two pieces of wire is 6 : 11. If the area of the
smaller star is 72 cm2 , find the area of the larger star.
16. The scale of the floor plan of a flat is 1 cm to 1.5 m. If the area of the sitting room on the floor plan is
8.1 cm2 , find its actual area.
[ In this exercise, give your answers correct to 1 decimal place if necessary. ]
17. Complete the following table. (Take   3.14 .)
Radius
Diameter
Circumference
5 cm
12.5 cm
20 cm
35 cm
157 cm
266.9 cm
10.39
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18. Find the perimeter of each of the following semi-circles. (Express your answers in terms of .)
(a)
(b)
A
(c)
5 cm
O
A
B
42 cm
B
A
12 cm
B
19. The following figures are formed by semi-circles, find the perimeter of each figure. (Express your
answers in terms of .)
(a)
A
(b)
A
B
5 cm
(c)
A
7 cm
11 cm
C
6 cm
B
4 cm
4 cm
D
C
5 cm
B
C
20. Find the perimeter of each of the following figures. (Express your answers in terms of .)
(a)
A
(b)
B
(c)
2 cm
A
B
B
C
6 cm
10 cm
The figure is formed by
semi-circles and a straight line.
4 cm
A
C
The figure is formed by
semi-circles and a straight line.
12 cm
O 15 cm C
D
The figure is formed by
quadrants and straight lines.
21. Given that the diameters of two circles are 14 cm and 16 cm respectively, what is the difference in
their circumferences? (Express your answer in terms of .)
22. The diameter of a wheel of a bicycle is 0.6 m. Find the distance travelled by the bicycle in
20 revolutions of the wheel.
23. The length of the minute-hand of a clock is 12 cm. Find the distance moved by the tip of the
minute-hand in 45 minutes. (Express your answer in terms of .)
24. Terry jogged around a circular park. Suppose he had completed 4 laps with a total distance of 1 250 m,
find the radius of the park.
10.40
 2009 Chung Tai Educational Press. All rights reserved.
25. A rope of 198 cm long can wrap around a cylindrical can 6 times. What is the diameter of the base of
the can?
26. A coin with the radius of 1.2 cm makes 3 revolutions per second on the ground. Find the speed of this
coin. (Express your answer in cm/s.)
27. The ratio of the circumferences of two circles is 7 : 5. What is the ratio of their diameters?
28. The diameter of a car wheel is 48 cm. If the wheel makes 550 revolutions per minute, find the speed
of the car. (Express your answer in km/h.)
29. The ratio of the circumferences of three circles is 7 a : 5b : 4c. What is the ratio of their radii?
30. The height and the circumference of the base of a right cylindrical container a re 20 cm and 30 cm
respectively. Can a square metal plate with the sides of 10 cm each be put into the container? Explain
briefly.
[ In this exercise, give your answers correct to 1 decimal place if necessary. ]
31. Complete the following table.
Radius
Diameter
Area
5 cm
8 cm
12 cm
30 cm
43 cm 2
95.2 cm 2
10.41
 2009 Chung Tai Educational Press. All rights reserved.
32. The following figures are formed by semi -circles and straight lines, find the area of each figure.
(Express your answers in terms of .)
A
(a)
4m
(b)
1m
A
3 cm
D
B
A
10 cm
B
8 cm
C
B
4 cm
(c)
1m
C
C
D
33. The following figures are formed by semi -circles, find the area of each figure. (Express your answers
in terms of .)
(a)
6 cm
(b)
A
A
B
4 cm
B
6 cm
C
(c)
D
C
4 cm
A
C
B
D
4 cm
6 cm
8 cm
4 cm
34. The following figure is formed by a quadrant and an isosceles right -angled triangle. Find the area of
the shaded region.
B
3 cm
A
3 cm
O
35. The diameter of a circular flying disc is 24 cm, find its area.
36. The area of a discus is 350 cm2 , find its radius.
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 2009 Chung Tai Educational Press. All rights reserved.
37. The figure is formed by a quadrant, a semi -circle and a straight line. If the area of the shad ed region is
100 cm2 , find the value of x.
x cm
38. The following figure is formed by quadrants and a square. Find the area of the shaded region.
A
D
2 cm
B
2 cm
C
39. If the radius of a circle decreases by 5%, what is the percentage decrease in the area of the circle?
40. The base areas of two cylindrical cakes are in the ratio of 9 : 16. Find the ratio of their base diameters.
41. In the figure, the ratio of the radii of two circles is 7 : 9.
(a) Find the ratio of the area of the smaller ci rcle to that of the larger circle.
(b) If the area of the shaded region is 48 cm2 , find the respective areas of the smaller circle and the
larger circle.
42. It is given that the length of a necklace is 50 cm. What is the area of the circle formed by the
necklace?
43. A circular lawn with the area of 42 m2 is surrounded by fences. Find the length of the fences.
10.43
 2009 Chung Tai Educational Press. All rights reserved.
44. In the figure, the door is formed by a semi -circle and a rectangle. If its area is (0.18  3) m2 , find its
height.
0.6 m
Height
45. In the figure, the width of the wooden frame is 1 cm. Find its area.
1 cm
15.24 cm
11.43 cm
A quadrant
46. The figure is formed by two squares and a circle.
12 cm
(a) Find the radius of the circle.
(b) Find the length of the side of the smaller sq uare. (Give your answer correct to 3 significant
figures.)
(c) Find the area of the shaded region. (Give your answer correct to 3 significant figures.)
10.44
 2009 Chung Tai Educational Press. All rights reserved.
47. Figure I and Figure II are formed by squares and quadrants.
10 cm
10 cm
B
A
Figure I
Figure II
(a) In Figure I,
(i) find the area of region A.
(ii) find the area of region B.
(b) Hence, find the area of the shaded region in Figure II.
(Express your answers in terms of .)
[ In this exercise, give your answers correct to 3 significant figures if necessary. ]

48. Find the length of AB in each of the following figures.
(a)
(b)
A
(c)
210
A
2 cm
O
B
B
3 cm
330
5 cm
2 cm
100
O
5 cm
O
A
3 cm
B
49. Find the area of sector AOB in each of the following figures.
B
(a)
(b)
(c)
A
6 cm
260
4.5 cm
35
A
6 cm
O
3 cm
115
O
3 cm
O
4.5 cm
A
B
B
10.45
 2009 Chung Tai Educational Press. All rights reserved.
50. Find the value of x in each of the following figures.
(a)
(b)
A
48 cm
8
cm
3
12 cm
x
A
x
O
12 cm
(c)
B
x
16 cm
O
A
40 cm O
40 cm
16 cm
B
B
Area  224 cm 2
51. Find the value of x in each of the following figures.
(a)
(b)
11 cm
(c)
30 cm
A
A
B
x cm
x cm
200
x cm
132
O
O
x cm
B
A
x cm
O
B
320
x cm
Area  72 cm2
52. An arc AB of a circle with the diameter of 25 cm subtends an angle of 45 at the centre. Find the
length of arc AB.
53. An arc AB of a circle with the diameter of 7 cm subtends 66 at the centre at O. Find the area of sector
AOB.
54. Find the perimeter of each of the following sectors.
Y
(a)
(b)
(c)
2 cm
Y
160
7 cm
X
40
X
2 cm
7 cm
O
10.46
 2009 Chung Tai Educational Press. All rights reserved.
O
210
X 1.2 cm O
1.2 cm
Y
55. In the figure, O is the centre of arc APC and arc BQD. AEB and
CFD are semi-circles. It is given that BOD  120, OA  6 cm
and AB  2 cm . Find the area of the shaded region.
B
Q
A
P
E
O
120
C
F
D
56. The
figure
shows
a
paper
fan,
where
OA  OD  8 cm,
AB  DC  15 cm and AOD  108 . Find the area of ABCD.
C
B
D
A
O
57. In the figure, O is the centre, the radius is 8 cm, AOB  90 .
(a) Find the area of the shaded region.
(b) Find the perimeter of the shaded region.
O
8 cm
A
B
58. The figure shows an equilateral triangle ABC with sides of 10 cm
 
C

each. D, E and F are mid-points of the sides of the triangle. A, B and
C are the centres of the arcs FD , DE and EF respectively.
F
E
(a) Find the area of the shaded region.
(b) Find the percentage of the shaded area in the figure.
A
D
B
10.47
 2009 Chung Tai Educational Press. All rights reserved.
59. An iron wire of length 100 cm is bent into a sector OAB as shown
in the figure.
A
B
(a) If AOB  30 , find the area of sector OAB.
(b) If OA  20 cm , find the area of sector OAB.
O
D
60. In the figure, OAC and OBD are two similar sectors. The area of
the shaded region is 30 cm2 . The length of OA is 4 times that of
AB.
C
(a) Find OB : OA .
O
A
(b) Find the area of sector OAC. (Express your answer in terms
of .)
61. The figure is formed by arc ACB and arc ADB, where O and P are
the centres of arc ACB and arc ADB respectively. Is a piece of
iron wire with the length of 40 cm enough to form the figure?
Explain briefly.
B
6 cm
C
120
O
(a) Find the perimeter of sector OAB.

of AB is
(b) If the length
answer in terms of .)
P
D
4 cm
A
62. In the figure, rectangle PQRS is formed by a wire. The wire is
now bent into sector OAB.
B
P
70
S
4 cm
B
A
9 cm
10 cm, find AOB . (Express your
O
Q
(c) Is the area of sector OAB equal to the area of rectangle
PQRS? Explain briefly.
10.48
 2009 Chung Tai Educational Press. All rights reserved.
R
 

63. In the figure, ABC is an equilateral triangle with sides of 20 cm each. The centres of B PC , A Q C and
A R B are A, B and C respectively. Find the area of the shaded region.
A
Q
R
20 cm
20 cm
20 cm
B
C
P
64. In the figure, OAB and PCD are sectors, Chris thought that
area of sector PCD
PD 2
(
) , do you
area of sector OAB
OB
agree? Explain briefly.
C
16 cm
A
B
8 cm
20
8 cm
40
O
D
16 cm
P
[ In this exercise, give your answers correct to 3 significant figures if necessary. ]
65. Complete the following table.
Base area of prism
10 cm
2
Volume of prism
5 cm
25 cm 2
150 cm
Height of prism
4 cm
2
600 cm 3
12 cm 2
180 cm 3
25 cm
900 cm 3
60 cm
1 080 cm 3
10.49
 2009 Chung Tai Educational Press. All rights reserved.
66. Find the volume of each of the following prisms.
8 cm
(a)
6 cm
(b)
(c)
7 cm
6 cm
10 cm
12 cm
11 cm
14 cm
3 cm
10 cm
67. The following are cylinder A and cylinder B. Find the difference in their volumes. (Express your
answer in terms of .)
2m
O
4m
O
4m
2m
Cylinder A
Cylinder B
68. A cylindrical cup with the base radius of 5 cm is filled with water. If 80 cubes with sides of 1 cm each
are immersed into the water without overflow,
(a) find the volume of a cube.
(b) find the rise in the water level.
69. The base diameter and the capacity of a cylindrical can are 6.5 cm and 330 cm3 respectively. Find the
height of the can.
70. A cylindrical metal bar with the radius of 3 cm and length of 5 cm is melted and recast into a pipe as
shown below. Find the length of the pipe.
3 cm
O
1 cm
10.50
 2009 Chung Tai Educational Press. All rights reserved.
71. Find the volume of each of the following prisms.
(a)
(b)
4 cm
(c)
10 cm
16 cm
2 cm
2 cm
2 cm
3 cm
24 cm
8 cm
2 cm
6 cm
2 cm
12 cm
10 cm
10 cm
16 cm
5 cm
72. There are 50 rectangular copper bars with dimensions 4 mm  5 mm  10 cm. They are melted and recast
into a large cuboid with the sides of its square base of 1 cm each. Find the height of the large cuboid.
73. The figure shows a copper coin with the diameter of 24 mm. In the centre of the coin, there is a square
hole with the sides of 5 mm each. If the total volume of 50 copper coins is 24 cm3, find the thickness
of each copper coin.
24 mm
5 mm
74. The figure shows the uniform cross -section of an L-shaped aluminium plate. Each aluminium plate is
120 cm long.
2 mm
40 mm
2 mm
40 mm
(a) Find the volume of a piece of L-shaped aluminium plate in cm 3 .
(b) It is known that the density of aluminium is 2.7 g/cm 3 . Is it enough to produce 20 pieces of
L-shaped aluminium plate with 10 kg of aluminium? Explain briefly.
10.51
 2009 Chung Tai Educational Press. All rights reserved.
75. The figure shows a spiral staircase with 4 steps. Each step is 15 cm high. The uniform cross -section of
each step is a sector with the angle at the centre of 30  and radius of 40 cm. Find the volume of the
spiral staircase.
40 cm
30
15 cm
15 cm
15 cm
15 cm
76. Water flows through a pipe with the inner diameter of 16 cm at a speed of 0.8 m/s.
(a) Find the volume of water flowing out from the pipe per second. (Express your answer in terms of .)
(b) The height and the base radius of a cylindrical tank are 1 m and 2 m respectively. Can the tank be
fully filled by the above pipe in 15 minutes? Explain briefly.
77. If both the base radius and the height of a cylinder increase by 10%, find the percentage incre ase in its
volume.
[ In this exercise, give your answers correct to 3 significant figures if necessary. ]
78. Find the total surface area of each of the following solids.
(a)
2 cm
(b)
2 cm
6 cm
4 cm
20 cm
(c)
1 cm
2 cm
14 cm
Cuboid
Cube
10.52
 2009 Chung Tai Educational Press. All rights reserved.
O
Cylinder
79. Find the total surface area of each of the following prisms.
(a)
6 cm
10 cm
(b)
(c)
5 cm
10 cm
12 cm
4 cm
12 cm
4 cm
10 cm
5 cm
4 cm
4.2 cm
10 cm
16 cm
3 cm
80. A metal cuboid with the length of 16 cm, width of 8 cm and height of 4 cm is melted and recast into a
cube. Find the total surface area of the cube.
81. The base radius and the height of a cylinder are r cm and h cm respectively. If the sum of the areas of
the two bases is equal to the curved surface area of the cylinder, find r : h.
82. The figure shows a cylindrical can with the diameter of 8 cm and capacity of 600 cm3 . A rectangular
packing paper is perfectly fit on the curved surface of the can. Find the area of the packing paper.
8 cm
83. The length, width and height of a room are 8 m, 6 m and 2.5 m respectively. The total area of a door
1
and a window occupies of the area of the walls in the room. If the ceiling and the walls are to be
5
painted,
(a) find the total painted area.
(b) Given that the capacity of a tin of paint is 2 L and each L of paint can paint an area of 6 m2, are
10 tins of paint enough to paint the room? Explain briefly.
10.53
 2009 Chung Tai Educational Press. All rights reserved.
84. (a) Figure I is formed by two semi-circles with the diameters of 3 cm each and a rectangle with
dimensions of 3 cm  6 cm . Find the area of Figure I.
(b) Figure II shows a candy can with the height of 10 cm, and its uniform cross -section is congruent to
Figure I. Given that one of its bases and the lateral surface are made of metal which cost 0.8 ¢/cm2 ,
and the other base is a plastic cover which cost 5 ¢ each. Find the cost to produce 1 000 candy cans.
(Give your answer correct to the nearest dollar.)
3 cm
10 cm
6 cm
Figure I
Figure II
85. Figure I and Figure II show two containers in the shapes of a cylinder and a square prism respectively.
Both the containers are with lids, their heights are both 10 cm, and their volumes are both 500 cm 3 . If
the material cost of making the containers is 0.1 ¢/cm 2 , which container has a lower material cost?
Explain briefly.
Figure I
Figure II
86. The diameter of a circle is 3.4 cm, correct to 2 significant figures.
(a) Find the upper limit and lower limit of the diameter.
(b) Find the possible range of the circumference. (Express your answer in terms of .)
10.54
 2009 Chung Tai Educational Press. All rights reserved.
87. The length and width of the cover of a book are 25 cm and 18 cm respectively, correct to the nearest cm.
(a) (i) Find the upper limit and lower limit of the length of the cover.
(ii) Find the upper limit and lower limit of the width of the cover.
(b) Find the possible range of the area of the cover.
88. The figure shows ABC, where AD  19 .4 cm and BC  24 .3 cm, correct to 3 significant figures.
A
B
D
C
(a) (i) Find the upper limit and lower limit of AD.
(ii) Find the upper limit and lower limit of BC.
(b) Find the possible range of the area of ABC.
89. The figure shows a prism with a trapezium base, where AB  2.4 m, AD  2.2 m, DC  3.0 m and
AF  3.2 m, correct to 1 decimal place.
F
G
A
B
E
H
D
C
(a) (i) Find the upper limit and lower limit of AB.
(ii) Find the upper limit and lower limit of AD.
(iii) Find the upper limit and lower limit of DC.
(iv) Find the upper limit and lower limit of AF.
(b) Is it possible for the actual volume of the prism to be 21 m3 ? Explain briefly.
10.55
 2009 Chung Tai Educational Press. All rights reserved.
90. The figure shows a pentagon ABCDE, where AB  10 cm, BC  8 cm, CD  26 cm and AE  24 cm ,
correct to the nearest cm.
A
B
E
C
D
(a) Find the lower limit of the area of pentagon ABCDE.
(b) If the actual area of pentagon ABCDE is x cm2, find the range of values of x.
91. The figure shows the floor plan of a flat.
A
F
E
B
D
C
(a) In the floor plan, measure the lengths of AB, AF, ED and CD. (Give your answers correct to the
nearest 0.1 cm.)
(b) Given that the scale of the floor plan is 1 cm : 1.2 m, can the area of the flat be 32 m 2 ? Explain
briefly.
10.56
 2009 Chung Tai Educational Press. All rights reserved.