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Mathematics Secondary 2. Chapter 1 Congruence and Similarity. Page 4

16. On a map the distance between two places A and B is 15 cm and the area of the Central Business District is 8 cm2. If the scale of the map is 1 : 80000,
(a) Find the actual distance of AB in km,
(b) Find the actual area of the Central Business District in km2.

17. The plans of a building are drawn to a scale of 1 : 150.
(a) Find the actual length, in metres, represented by 42 cm on the plan.
(b) The actual length of the diagonal of a hall is 33 m. Find its lenth, in cm, on the plan.
(c) The area of a meeting room is 450 m2. Find its area, in cm2, on the plan.

18. The diagram shows a triangle ABC where AB = 4 km, AC = 3 km and BC = 5 km. If  triangle ABC is drawn on a map of scale 1 : 50000, find
(a) the length of AB, in cm, on the map,
(b) the area of triangle ABC, in cm2, on the map.

19. A football stadium is represented by a scale of 1 cm to 8 m on paper.
(a) Find the actual length of the field if the length on the drawing is 28 cm.
(b) The actual width of the stadium is 120 m. Find its width on the diagram.
(c) If the area of the seating gallery is 960 m2. Find its area on the drawing.

20. The area scale of a map is 1 : 16000000. The length of two places A and B on the map is 8 cm and the area of a private housing estate is 12 cm2.
(a) Find the linear scale of the map in the form 1 : n.
(b) Find the actual distance of AB in metres.
(c) What is the area of the private housing estate in hectares?