Final answer:
To find the map scale, calculate the actual area in square meters and the map area in square centimeters, then divide the actual area by the map area after converting square centimeters to square meters. The actual area is 3517 hectares or 35,170,000 m2, the map area is 3.9 cm2, resulting in a scale approximately 1:901,282.
Step-by-step explanation:
To find the value of n in the scale 1:n, we need to relate the map area to the actual area of the estate. The actual area is 3517 hectares (ha), which we convert to square meters since the metric units on the map will relate to square centimeters. There are 10,000 square meters in one hectare, so the actual area in square meters is 3517 ha × 10,000 m2/ha = 35,170,000 m2.
Next, we need to calculate the area of the estate on the map. The map dimensions are 2.6 cm by 1.5 cm, so the map area in square centimeters is 2.6 cm × 1.5 cm = 3.9 cm2.
To find the scale factor n, we divide the actual area by the map area:
3517 ha = 35,170,000 m2
3.9 cm2 on the map corresponds to 35,170,000 m2 in reality.
1 cm2 on the map corresponds to 35,170,000 m2 / 3.9 cm2 in reality.
n = 35,170,000 m2 / 3.9 cm2
We need to convert square centimeters to square meters to match the units (1 m2 = 10,000 cm2). So:
n = 35,170,000 m2 / (3.9 cm2 × 10,000)
n = 35,170,000 m2 / 39,000 cm2
n = 901,282.0512820513
Therefore, the scale of the map is approximately 1:901,282.