A soccer field is a rectangular in shape and is 100 meters long and 75 meters wide. The hectare is a metric unit of area after used to measure larger areas. Given that 1 hectare = 10,000 meters3, which of the following represents the soccer field’s area in hectares?
A.
7.5 hectares
B.
75,000,000 hectares
C.
0.75 hectares
D.
7,500 hectares
The correct answer and Explanation is :
To calculate the area of a soccer field in hectares, let’s first find the area in square meters.
Step 1: Calculate the area of the soccer field in square meters.
The soccer field is a rectangle with a length of 100 meters and a width of 75 meters. The area ( A ) of a rectangle is given by the formula:
[
A = \text{Length} \times \text{Width}
]
Substituting the values:
[
A = 100 \, \text{m} \times 75 \, \text{m} = 7,500 \, \text{m}^2
]
Step 2: Convert square meters to hectares.
We know that 1 hectare is equal to 10,000 square meters. To convert the area of the soccer field from square meters to hectares, divide the area in square meters by 10,000:
[
\text{Area in hectares} = \frac{7,500 \, \text{m}^2}{10,000 \, \text{m}^2/\text{hectare}} = 0.75 \, \text{hectares}
]
Step 3: Choose the correct answer.
The area of the soccer field is 0.75 hectares. Therefore, the correct answer is:
C. 0.75 hectares
Explanation:
- A soccer field is 7,500 square meters in size. To convert this to hectares, divide by 10,000 because 1 hectare equals 10,000 square meters. The result is 0.75 hectares, which is significantly smaller than options A, B, or D.
- Option A (7.5 hectares) and option D (7,500 hectares) would represent much larger areas than the actual soccer field size, while option B (75,000,000 hectares) is unreasonably large and incorrect.