To find the area of the green square, we can use the areas of the red and yellow squares.
The area of the red square is 16, which means its side length is: \[ \sqrt{16} = 4 \text{ ft} \]
The area of the yellow square is 25, which means its side length is: \[ \sqrt{25} = 5 \text{ ft} \]
Assuming the green square's area is related to the others, by some arithmetic operation between the areas of the red and yellow squares, we can calculate based on typical geometric relationships involving squares, such as perhaps the area of the green square being the sum of the two areas.
So, if we add the areas: \[ 16 + 25 = 41 \]
However, 41 is not one of the answer choices. To look more closely, perhaps the area of the green square could be determined based on a geometric configuration like a larger square from which the other squares are subtracted. Without further context on their arrangement, a common configuration might yield the area of the larger square formed by the two.
Another possibility is that the area of the green square is related to the combination of the first two.
If we consider:
Area of green square = Area of red square + Area of yellow square + x (which could potentially be the product of their roots)
We get the area could be low numbers or multiply so it could not likely be 128. However 9, 81, and 256 could make some geometric sense if we looked for a square that scales or combines to those numbers.
Looking at the answers again, it seems most intuitive that you might be looking for a basic geometric equality or adjacency of areas that might lead us to
- 81 ft² which is the product of both square lengths (4 * 5) Calculating now:
Then considering the product of the two square's areas:
4ft (length of red) * 5ft (length of yellow) = 20
While this is more complicated than needed could not be the approach on its own but seems we haven’t hit the sweet spot.
This leads us to conclude that area corresponding in traditional counting measure could relate closer to common simplest for known additive:
Thus, the area of the green square based on common tests applied for basic combinations of manageable outputs that yield full segments in simplest results would hence most likely lead up:
Thus, B: 9 ft².
Let’s look critically to ensure it to be certain for clarity with any geometric outlines.
If this can aid significantly further, please provide less or more direct context with configuration!