1. **Problem Statement:** We have a map with points Q, P, A, and B arranged in a rectangular grid with given distances. We need to draw an accurate map using a suitable scale and determine the areas of the regions formed. 2. **Understanding the Data:** The distances given are: - PQ = 450 metres (vertical distance between P and Q) - Horizontal distances: Q to 300 (left), P to 100 (left), 200 B (right), 90 A (right) - Vertical distances inside the grid: 450, 400, 330, 180, 80 3. **Choosing a Scale:** To fit the map nicely, choose a scale such as 1 cm = 50 metres. 4. **Drawing the Map:** - Draw vertical line PQ of length $$\frac{450}{50} = 9\text{ cm}$$. - Mark points Q at top and P at bottom. - From Q, move left 6 cm (300/50) to mark Q 300. - From P, move left 2 cm (100/50) to mark P 100. - From the center vertical line, move right 4 cm (200/50) to mark B. - From the center vertical line, move right 1.8 cm (90/50) to mark A. 5. **Determining Areas:** - The rectangular grid can be divided into two rectangles: - Left rectangle between Q 300 and P 100: width = 6 cm - 2 cm = 4 cm, height = 9 cm - Right rectangle between A and B: width = 4 cm - 1.8 cm = 2.2 cm, height = 9 cm - Calculate areas in square cm: - Left area = $$4 \times 9 = 36\text{ cm}^2$$ - Right area = $$2.2 \times 9 = 19.8\text{ cm}^2$$ - Convert areas back to square metres: - 1 cm = 50 m, so 1 cm² = $$50^2 = 2500\text{ m}^2$$ - Left area = $$36 \times 2500 = 90000\text{ m}^2$$ - Right area = $$19.8 \times 2500 = 49500\text{ m}^2$$ 6. **Final Answer:** - Left region area = 90000 square metres - Right region area = 49500 square metres This completes the accurate drawing and area determination using the scale 1 cm = 50 metres.