The following diagram shows a triangle
with sides 5 cm, 7 cm, 8 cm.
7
5
diagram not to scale
Determine if this could be a right triangle.
8
No, it could not.
1
The diagram shows a rectangular prism 22.5 cm
by 40 cm by 30 cm.
H
E
G
Calculate the length of [AC].
37.5 cm
F
40 cm
D
C
30 cm
2
A
22.5 cm
B
x = 1.28 m
3
4.70 m
4
How high is the roof above the walls in the following
roof structure?
4.54 m
5
The following diagram shows a carton in
the shape of a cube 8 cm long on each
side:
(a) The longest rod that will fit on the bottom of the
carton would go from E to G. Find the length l of
this rod.
(b) Find the length L of the longest rod that would
fit inside the carton.
B
C
D
A
F
6
B
G
H
= 11.3 cm
= 13.9 cm
A square garden with sides 100 m is divided into
two triangular plots by a fence along one diagonal.
a) What is the length of the fence in meters?
141 m
b) If the fence costs $15.50 per meter, what is the
total cost?
$2192
7
Colin believes he has cut out a perfect rectangular
canvas covering which has adjacent sides 8.6 m and
5.4 m. The opposite sides are equal. He measures a
diagonal to be 10.155 m. Is Colin’s rectangle right
angled? (support your answer)
yes
8
In the diagram below, PQRS is the square base
of a solid right pyramid with vertex V. The
sides of the square are 8 cm, and the height
VG is 12 cm. M is the midpoint of [QR].
Diagram not to scale(a)Write down the length of [GM]
= 4 cm
V
(b) Calculate the length of [VM].
= 12.6 cm
P
Q
G
S
9
8 cm
8 cm
M
R
Two ships B and C leave a port A at the same time. B
travels in a direction 067 at a constant speed of 36
km/h. C travels in a direction 157 at a constant speed
of 28 km/h.
Find the distance between them after 2 hours.
91.2 km
10
OABCD is a square based pyramid of side 4 cm.
The vertex D is 3 cm directly above X, the centre of
square OABC.
M is the midpoint of AB.
= 2 cm
(a)Find the length of XM.
11
(b) Calculate the length of DM.
= 3.61 cm
D
Diagram
not to scale
B
C
X
O
M
A
A rhombus has sides of length 8 cm. One
of its diagonals is 15cm long. Find the
length of the other diagonal.
= 2.78 cm
12
Find the value of any unknown.
x  29  5.39cm
y  45  6.71cm
13
1
4
A sailing ship sails 46 km North and then 74
km East.
How far is the ship from its starting point?
= 87.1 km
An isosceles triangle has equal sides of
length 8 cm and a base of length 6 cm.
Find the area of the triangle.
22.2 cm2
15