To find the area of a rectangle (in this case, a table), we multiply the length by the width.
The length of the table is \( 4 \frac{1}{2} \) feet, which can be converted to an improper fraction:
\[ 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \text{ feet} \]
The width of the table is \( 2 \frac{1}{4} \) feet, which can also be converted to an improper fraction:
\[ 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \text{ feet} \]
Now, we can calculate the area:
\[ \text{Area} = \text{Length} \times \text{Width} = \left(\frac{9}{2}\right) \times \left(\frac{9}{4}\right) \]
To multiply these fractions, we multiply the numerators and the denominators:
\[ \text{Area} = \frac{9 \times 9}{2 \times 4} = \frac{81}{8} \text{ square feet} \]
Now, we can convert \( \frac{81}{8} \) to a mixed number.
Dividing \( 81 \) by \( 8 \) gives \( 10 \) with a remainder of \( 1 \): \[ 81 \div 8 = 10 \quad \text{(whole number)} \] \[ 81 - (10 \times 8) = 1 \quad \text{(remainder)} \]
So, we can express \( \frac{81}{8} \) as:
\[ 10 \frac{1}{8} \text{ square feet} \]
Thus, the area of the table is:
\[ \boxed{10 \frac{1}{8}} \text{ square feet} \]