1. 1 The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm. diagram not to scale Determine if this could be a right triangle. No, it could not.

2. 2 The diagram shows a rectangular prism 22.5 cm by 40 cm by 30 cm. Calculate the length of [AC]. 37.5 cm

3. 3 x = 1.28 m

4. 4 4.70 m

5. 5 How high is the roof above the walls in the following roof structure? 4.54 m

6. = 11.3 cm 6 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. = 13.9 cm

7. 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. 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. 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]. = 4 cm = 12.6 cm

10. 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

11. 11 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. (a)Find the length of XM. (b)Calculate the length of DM. O C D A M B X Diagram not to scale = 2 cm = 3.61 cm

12. 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. 13 Find the value of any unknown.

14. 14141414 A sailing ship sails 46 km North and then 74 km East. How far is the ship from its starting point? = 87.1 km

15. 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 cm 2