1

The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm.

5 7

8

diagram not to scale

Determine if this could be a right triangle.

No, it could not.

2

The diagram shows a rectangular prism 22.5 cm by 40 cm by 30 cm.

H G

E F

A B

D C

4 0 cm

3 0 cm

2 2 .5 cm

Calculate the length of [AC].

37.5 cm

3

x = 1.28 m

4

4.70 m

5

How high is the roof above the walls in the following roof structure?

4.54 m

= 11.3 cm

6

The following diagram shows a carton in the shape of a cube 8 cm long on each side:

B C

B H

AD

GF

(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.

= 13.9 cm

7

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?

b) If the fence costs $15.50 per meter, what is the total cost?

141 m

$2192

8

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

9

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].

(b) Calculate the length of [VM].V

P

G

Q

M

RS 8 cm

8 cm

= 4 cm

= 12.6 cm

10

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

11OABCD 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.(a)Find the length of XM.

(b) Calculate the length of DM.

O

C

D

A

M

B

X

Diagramnot to scale

= 2 cm

= 3.61 cm

12

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

13

Find the value of any unknown.

29 5.39x cm

45 6.71y cm

14A sailing ship sails 46 km North and then 74 km East.How far is the ship from its starting point?

= 87.1 km

15

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