To find the area of the pavilion in square feet, we need to divide the total number of bricks by the number of bricks per square foot.
Given:
- Total number of bricks = \(2.967 \times 10^5\)
- Bricks per square foot = \(6.9\)
We can calculate the area in square feet as follows:
\[ \text{Area} = \frac{\text{Total number of bricks}}{\text{Bricks per square foot}} = \frac{2.967 \times 10^5}{6.9} \]
Calculating this step-by-step:
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Divide the coefficients: \[ \frac{2.967}{6.9} \approx 0.430 \]
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Subtract the exponents (since we're dealing with powers of 10): \[ 10^{5 - 0} = 10^5 \]
So the area in scientific notation is:
\[ 0.430 \times 10^5 \]
Now, to express \(0.430\) in proper scientific notation, we can convert it to \(4.30 \times 10^{-1}\):
\[ 0.430 \times 10^5 = 4.30 \times 10^{-1} \times 10^5 = 4.30 \times 10^{4} \]
Now, we can compare with the given options:
- \(4.3 \times 10^4\)
- \(2.33 \times 10^5\)
- \(0.43 \times 10^4\)
The correct conversion leads us to \(4.3 \times 10^4\).
Therefore, the area of the pavilion is:
\[ \boxed{4.3 \times 10^4 \text{ square feet}} \]