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

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. 1. The diagram shows a rectangular prism 22.5 cm by 40 cm by 30 cm. Calculate the length of [AC]. 37.5 cm. 2. x = 1.28 m. 3.

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

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  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. 1

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

  3. x = 1.28 m 3

  4. 4.70 m 4

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

  6. The following diagram shows a carton in the shape of a cube 8 cm long on each side: • 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. = 11.3 cm = 13.9 cm 6

  7. A square garden with sides 100 m is divided into two triangular plots by a fence along one diagonal. What is the length of the fence in meters? If the fence costs $15.50 per meter, what is the total cost? 141 m $2192 7

  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 8

  9. V P Q 8 cm G M S R 8 cm 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 • Write down the length of [GM]. (b)Calculate the length of [VM]. = 4 cm = 12.6 cm 9

  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 10

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

  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 12

  13. Find the value of any unknown. 13

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

  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 15

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