Area Calculation: Finding Total Surface Area of 3/8 and 1/4 Fractions in 10,000m²

To solve this problem, we'll follow these steps:

• Step 1: Identify the area covered by the banana plantation.

• Step 2: Identify the area covered by the watermelon plantation.

• Step 3: Sum the two areas to find the total area covered by both plantations.

Now, let's work through each step:
Step 1: The banana plantation covers $\frac{3}{8}$ of the field.
Calculate its area: $10,000 \times \frac{3}{8} = 10,000 \times 0.375 = 3,750 \, \text{m}^2$.

Step 2: The watermelon plantation covers $\frac{1}{4}$ of the field.
Calculate its area: $10,000 \times \frac{1}{4} = 10,000 \times 0.25 = 2,500 \, \text{m}^2$.

Step 3: Add these areas to find the total area covered by both plantations:
$3,750 \, \text{m}^2 + 2,500 \, \text{m}^2 = 6,250 \, \text{m}^2$.

Therefore, the total surface area covered by the banana and watermelon plantations is 6,250$\text{m}^2$.