27. A soccer field is rectangular in shape and measures 100 meters in length and 75 meters in width. The hectare is a metric unit of area often used to measure large areas. Given that 1 hectare = 10,000 square meters, what is the soccer field's area in hectares?
Answer: D
The soccer field's area is 0.75 hectares.
To find the area of the soccer field in hectares, we first calculate the area in square meters by multiplying the length and width of the field, which gives us 100 m * 75 m = 7,500 square meters. Since 1 hectare is equal to 10,000 square meters, we convert the area to hectares by dividing 7,500 by 10,000, resulting in 0.75 hectares.
A) 7,500 hectares
This option is incorrect because it suggests a total area that is 10,000 times larger than the actual area of the soccer field. The calculation of 7,500 hectares would imply a field area of 75,000,000 square meters, which is impossible given the dimensions provided.
B) 7.5 hectares
This option is also incorrect. While it is a plausible figure if miscalculated, 7.5 hectares would correspond to an area of 75,000 square meters, which exceeds the actual area of the soccer field of 7,500 square meters.
C) 75,000,000 hectares
This option is clearly incorrect as it represents an astronomically large area that is not feasible for a soccer field. This figure would indicate an area of 750,000,000,000 square meters, far beyond the dimensions of any standard soccer field.
D) 0.75 hectares
This option is correct as it accurately reflects the area of the soccer field calculated from its dimensions. By dividing the area of the field, 7,500 square meters, by 10,000 square meters per hectare, we arrive at 0.75 hectares.
Conclusion
The correct answer is 0.75 hectares, as it is the only option that accurately represents the area of the soccer field when converted from square meters to hectares. All other options significantly overstate the area, demonstrating a misunderstanding of the conversion from square meters to hectares.