To find the area of a regular octagon given its apothem and perimeter, we can use the following formula:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{Apothem} \times \text{Perimeter} \][/tex]
We have the following values:
- Apothem (\(a\)) = 10 inches
- Perimeter (\(P\)) = 663 inches
Using these values in the formula, we get:
[tex]\[ \text{Area} = \frac{1}{2} \times 10 \, \text{in} \times 663 \, \text{in} \][/tex]
Now, calculate the multiplication inside the formula:
[tex]\[ 10 \times 663 = 6630 \][/tex]
Next, multiply this result by \(\frac{1}{2}\):
[tex]\[ \frac{1}{2} \times 6630 = 3315 \][/tex]
So, the area of the octagon is:
[tex]\[ 3315 \, \text{square inches} \][/tex]
Among the given options, none of them directly matches our calculated area. However, the calculation confirms that the area of the octagon is [tex]\(3315 \, \text{square inches}\)[/tex].
