To find the area of the base \( B \) of a rectangular prism, we use the formula:
\[ B = \text{length} \times \text{width} \]
The given dimensions are:
- Length = \( 6 \frac{1}{4} \) meters
- Width = \( 5 \frac{1}{2} \) meters
First, we convert the mixed numbers into improper fractions.
For the length:
\[ 6 \frac{1}{4} = 6 + \frac{1}{4} = \frac{6 \times 4}{4} + \frac{1}{4} = \frac{24}{4} + \frac{1}{4} = \frac{25}{4} \]
For the width:
\[ 5 \frac{1}{2} = 5 + \frac{1}{2} = \frac{5 \times 2}{2} + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2} \]
Now we calculate the area \( B \):
\[ B = \frac{25}{4} \times \frac{11}{2} \]
To multiply the fractions, we multiply the numerators and the denominators:
\[ B = \frac{25 \times 11}{4 \times 2} = \frac{275}{8} \]
Next, we convert \( \frac{275}{8} \) into a mixed number. We divide 275 by 8:
\[ 275 \div 8 = 34 \quad \text{(whole number part)} \] \[ 275 - (34 \times 8) = 275 - 272 = 3 \quad \text{(remainder)} \]
So, we can write:
\[ \frac{275}{8} = 34 \frac{3}{8} \]
Thus, the area of the base of the rectangular prism is:
\[ \boxed{34 \frac{3}{8}} \text{ square meters} \]