To find the area of the rectangle-shaped flag, you can use the formula for the area of a rectangle:
\[ \text{Area} = \text{base} \times \text{height} \]
In this case, the base is 4.5 feet and the height is 2.5 feet:
\[ \text{Area} = 4.5 , \text{ft} \times 2.5 , \text{ft} = 11.25 , \text{ft}^2 \]
Now, if you want to find the area squared, you simply square the area:
\[ \text{Area squared} = (11.25 , \text{ft}^2)^2 = 126.5625 , \text{ft}^4 \]
Thus, the area of the flag squared is \( 126.5625 , \text{ft}^4 \).