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Mathematics
Stage 5
Shape & Space
S. J. Cooper
Geometry (3) Construction of triangles
Remember do not remove any construction lines or arcs.
1. Draw a triangle ABC whose sides are AB = 7 cm , AC = 5 cm and BC = 4 cm.
Measure and write down the size of angle A.
2. Draw a triangle LMN whose sides are LM = 9 cm , MN = 4 cm and LN = 7 cm.
Measure and write down the size of angle N.
3. Draw a triangle PQR whose sides are PQ = 4 cm , PR = 4 cm and QR = 6 cm.
Measure and write down the size of angle Q.
4. Draw a triangle DEF whose sides are DE = 8 cm , EF = 5 cm and DF = 7 cm.
Measure and write down the size of angle D.
5. Draw a triangle ABC whose sides are AB = 5.4 cm , AC = 3.7 cm and BC = 6.3 cm.
Measure and write down the size of angle C.
6. Draw a triangle XYZ whose sides are XY = 7.2 cm , XZ = 6.2 cm and YZ = 9.4 cm.
Measure and write down the size of angle Z.
7. Draw a triangle LMN whose sides are LM = 4.8 cm , MN = 5.5 cm and LN = 11 cm.
Measure and write down the size of angle N.
8. With the aid of compasses, protractor, rulers, etc...
Draw accurately the following triangles and find the lengths required.
(a) (b) (c)
Angle E = ? Angle P = ? Angle M = ?
3 cm
4 cm
E
6.2 cm
2 cm
7.2 cm 10.4 cm 4 cm
13.4 cm
L
M
N
P
R
Q
9.1 cm
Geometry (4) Construction of triangles
REMEMBER DO NOT REMOVE ANY CONSTRUCTION LINES OR ARCS.
Use Pencil, Ruler, Compass and protractor for questions 1 to 5.
1. Draw a triangle ABC whose side AB = 7 cm and angles BAC = 40 and ABC = 50
Measure and write down the length of side BC.
2. Draw a triangle XYZ , where XY = 4 cm , ZXY = 70 and ZYX = 70 .
Measure and write down the length of ZX.
3. Draw a triangle DEF where DE = 6 cm , EDF = 54 and DEF = 31 .
Measure and write down the length of EF.
4. Draw a triangle PQR where PQ = 4.2 cm , PQR = 35 and QPR = 117 .
Measure and write down the length of side QR.
5. Draw an accurate drawing of the triangle opposite.
Use Pencil, Ruler and Compass only for questions 6 to 10.
6. Draw a triangle PQR where PQ = 3 cm , 90 = RQP and 30 = RPQ .
Measure and write down the length of side QR.
7. Draw a triangle BCD where BC = 8.4 cm , 15 = DCB and 60 = DBC .
Measure and write down the length of side BD.
8. Draw a triangle HIJ where HI = 6.7 cm , 75 = JHI and 60 = JIH .
Measure and write down the length of side IJ.
9. Draw a triangle ABC where AB = 5 cm , 120 = CBA and 30 = CAB .
Measure and write down the length of side AC.
10. Draw a triangle DEF where DE = 7.3 cm , 45 = FDE and 30 = FED .
Measure and write down the length of side DF.
4.6 cm
24 107
Geometry (5) Construction of triangles
REMEMBER DO NOT REMOVE ANY CONSTRUCTION LINES OR ARCS.
Use pencil, ruler, compass and protractor for questions 1 to 5.
1. Draw a triangle LMN where LM = 4 cm , 30 = NML ˆ and MN = 5 cm.
Measure and write down the length of LN.
2. Draw the triangle PQR where PQ = 7 cm, 70 = RPQ ˆ and PR = 4 cm.
Measure and write down the size of RQP .
3. Draw a triangle JKL where JK = 5 cm , 55 = LKJ ˆ and KL = 5.6 cm.
Measure and write down the length of JL.
4. Draw the triangle XYZ where XY = 3.8 cm, 125 = ZXYˆ and XZ = 5.1 cm.
Measure and write down the size of ZYX ˆ .
5. Draw a triangle ABC where AB = 4.3 cm , ABC = 45 and BC = 5.6 cm.
Measure and write down the length of AC.
Use pencil, ruler and compass only for questions 6 to 13.
6. Draw the triangle DEF where DF = 5.3 cm, 60 = EFD and FE = 6.4 cm.
Measure and write down the size of FDE .
7. Draw a triangle STU where ST = 10.7 cm , 45 = UST and SU = 8.5 cm.
Measure and write down the length of TU.
8. Draw the triangle EFG where EF = 9.4 cm, 30 =G FE and FG = 6.7 cm.
Measure and write down the size of EGF ˆ .
9. Draw the triangle PQR where PQ = 8.4 cm, 135 = RQP and QR = 4.7 cm.
Measure and write down the size of EGF ˆ .
10.Draw the triangle EFG where EF = 3.4 cm, 15 =G FE and FG = 5.5 cm.
Measure and write down the size of EGF ˆ .
11. Construct rectangle ABCD where AB = 9 cm and BC = 4 cm.
State the length of the diagonal AC.
12. Construct a rectangle which has dimensions 5.3cm by 11.7cm.
13. Construct rectangle LMNO where LM = 3.9 cm and MN = 6.8 cm.
State the length of the diagonal MO.
14. Construct a rectangle which has dimensions 10.3cm by 5.2cm.
Geometry (6) Pythagoras Theorem
1. Work out the length of the hypotenuse for each of the following, giving your answers correct to
1 decimal place. [all measurements are in centimetres]
(a) (b) (c)
(d) (e) (f)
(g) (h) (i) (j)
Work out the required lengths for each of the following, giving your answers to 2 decimal places.
2. Find a 3. Find b
4. Find AC 5. Find EF
6. Find PR 7. Find LM
2
7
6
6 9
8
4
9
7
5
4
6
3
14 13
5
11
10
21
8
a b
c
d e
f
g
h
i j
7cm
9cm
a 5cm
11cm
b
16cm
10cm
A
C B
12cm
15cm
D E
F
7cm 7cm
R P
Q 6.3m
4.5m
L
M N
8. Find p 9. Find x
10. Find AC
11. Find the length of the diagonal in the rectangle below:
12. Find the sloped edge, XY, on the isosceles triangle drawn below.
13. A ladder is placed up against the side of a house so that it reaches a height of 12m. If the
distance from the foot of the ladder to the base of the house is 2m, what is the length of the
ladder?
5.9cm
14.3cm
p
10.5m
9.8m
A
C B
17 cm 20cm
x
10 cm
30 cm
X
Z
Y
10 cm
8 cm
Geometry (7) Pythagoras Theorem II
1. Work out the length of the lettered side for each of the following, giving your answers
correct to 1 decimal place. [all measurements are in centimetres]
(a) (b) (c)
(d) (e) (f)
(g) (h) (i) (j)
Work out the required lengths for each of the following, giving your answers to 2 decimal places.
2. Find m 3. Find p
4. Find AB 5. Find DE
6. Find PQ 7. Find MN
12 6
a
8
11 c
9
4
b
7
10 f
13
5
e 3
6
d
3
14
j 18
7
h
15
10
i
20
6
g
15cm
12cm
m 5cm 11cm
p
8cm
10cm
A
C B
25cm 15cm
D E
F
14cm
7cm
R P
Q
8.1m 3.7m
L
M N
8. Find c 9. Find x
10. Find JK
11. Find the height of the isosceles triangle drawn below.
12. A ladder, of maximum length 5.4m, is placed up against the side of a house. If the distance
from the foot of the ladder to the base of the house is 2m, how high up the side of the house
will the ladder reach?
5.9cm 14.3cm
c
10.5m
5.4m
J
L K
13 cm
19cm
x
16 cm 16 cm
S
U
T
h cm
10 cm
Geometry (8) Area & perimeter II
1. Calculate the area for each of the following circles, giving your answers correct to 1 decimal place.
(a) (b) (c) (d)
2. Calculate the area of each of the following circles giving your answers correct to 2 decimal places.
(a) (b) (c) (d)
3. Which has the greater area, a circle with radius 9cm or a square with side 15cm?
4. Given the area of a circle is 54cm2 find its radius correct to 2 decimal places.
5. Find the area of the semicircle drawn opposite, giving
your answer to 2 decimal places.
6. Find the area of the shape opposite, giving your
answer correct to 1 decimal place.
7. Calculate the shaded area for each of the following shapes. [giving your answers correct to 2 significant
figures]
(a) (b) (c)
8. A circle has an area of 125 cm2. Calculate the length of its radius, giving your answer to 2 decimal
places.
5m 14cm 14cm 54m
3.7m 7.2cm 75m 60km
36 cm
100 cm
32 cm
12cm 6cm 5m 12m
7m
Geometry (9) Circumference of a circle
1. Calculate the circumference of each of the following circles, giving your answers correct to one decimal
place.
(a) (b) (c) (d)
2. Calculate the circumference of each of the following circles, giving your answers correct to 2 decimal
places.
(a) (b) (c) (d)
3. Find the perimeter of the semicircle drawn opposite,
giving your answer to 2 decimal places.
4. (a) What is the perimeter of a circle of diameter 70 metres (correct to 2 decimal places)?
The diagram is of a running track with “straights” of length
150m and with semicircular ‘bends’ which have diameter
70m.
(b) What is the length of one complete lap?
(c) How many laps (approximately) must an athlete run in a race of 10 000m?
5. A bicycle wheel has diameter 75cm. Calculate its circumference, giving your answer correct to the
nearest whole number.
6. What is the diameter of a circle whose circumference is 24cm? [Give your answer correct to 1 decimal
place].
7. What is the circumference of a circle whose area is 60cm2? {give your answer correct to the nearest
whole number]
8. Which has the greatest perimeter, a circle with radius 6cm or a square with side 5cm?
7cm 23m 19cm 43m
6.1m 2.3cm 112m 38m
50 cm
150m
70m
Geometry (10) Area of an Arc
1. Find the area for each of the following arcs, giving your answers correct to 1 decimal place
a) b)
c) d)
e) f)
g) h)
i) J)
2. Find the area of the shape drawn below
Geometry (11) Arc length
1. Find the length of the arc for each of the following, giving your answers correct to 1 decimal place.
a) b) c)
d) e) f)
g) h) i)
2. Find the perimeter for each of the following, giving your answers correct to 2 decimal places.
a) b) c)
3. Find the perimeter for the shape drawn below, giving your answer correct to 1 decimal place.
Geometry(12) Surface Area
1. Calculate the surface area for each of the following shapes
(a) (b) (c)
(d) (e) (f)
2. Work out the total surface area of the tin drawn below.
3. Calculate the surface area of the shape drawn
opposite.
12cm
4cm 7cm
5cm
20cm
40cm
40cm
18cm
14cm
8cm
8cm
15cm 2.3cm
1.1cm
2.7cm
2.4cm
10.5cm
8cm
7cm
6cm
8cm
6cm
Geometry(13) Similar and Congruent Shapes 1. From the selection below identify the two shapes which are congruent.
2. The two triangles are congruent.
Label the missing values.
3. Show that the two triangles ABC and ADE are similar.
Hence find the length of DC.
4. In each of the following finds the length of the lettered side, given that each pair of shapes are
similar.
(a)
(b)
(c)
5. Show that triangle ABC is similar to triangle ADE
Hence work out the length of (i) DE
(ii) CE
6. Show that the two triangles are similar
5 cm
9 cm
a
27 cm
b
6 cm
9cm
27
c
7 cm
8 cm 6
d
4cm
A
E C
D
B
10cm
9cm
3cm
7cm
