To find the area of a regular octagon, you can use the formula for the area of a regular polygon:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{Apothem} \times \text{Perimeter} \][/tex]
Here, we are given:
- The apothem (a) = 10 inches
- The perimeter (P) = 66.3 inches
Let's plug these values into the formula:
1. First, calculate the product of the apothem and the perimeter:
[tex]\[ \text{Product} = 10 \times 66.3 = 663 \][/tex]
2. Next, multiply this product by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ \text{Area} = \frac{1}{2} \times 663 = 331.5 \][/tex]
So, the area of the regular octagon is 331.5 square inches.
3. Finally, we need to round this result to the nearest square inch:
[tex]\[ \text{Rounded Area} = 332 \text{ square inches} \][/tex]
Therefore, the area of the octagon, rounded to the nearest square inch, is:
332 square inches
So, the correct option is:
[tex]\[ \boxed{332 \text{ in}^2} \][/tex]
