11 Problem-solving / Reasoning The diagram shows a hexagonal pyramid. The base is a regular hexagon. Q11 hint Hexagonal base: 5 cm Sketch one face. What type of triangles are the faces? 2.5 cm Construct the net of a hexagonal pyramid using a ruler and compasses. 12 Real The diagram shows the loci of two water sprinklers on a football pitch. A B a Copy the diagram and shade the intersection. b Describe what happens in the shaded area. 13 Real The diagrams show the watering systems for four flower beds. Each flowerbed has sprinklers that can move along rails. From any point on its rail, each sprinkler can reach plants up to 4 m away. a b 1m 1m 1m 10 m 10 m 10 m c 10 m 2m 10 m 10 m For each flower bed i copy the diagram ii construct and shade the locus of points the sprinklers can reach. Use centimetre squared paper and a scale of 1 cm to 1 m. iii Which system waters the largest area of the flowerbed? 14 a Construct this triangle. b Measure the hypotenuse. c Use Pythagoras’ theorem to check your answer. A 8 cm B 169 10 cm C