To calculate the area of a regular octagon given its apothem and perimeter, you can use the formula for the area of a regular polygon:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} \][/tex]
Given data:
- Apothem ([tex]\(a\)[/tex]) = 10 inches
- Perimeter ([tex]\(P\)[/tex]) = 66.3 inches
Let's go through the calculation step-by-step:
1. First, multiply the perimeter by the apothem:
[tex]\[ \text{Perimeter} \times \text{Apothem} = 66.3 \times 10 = 663 \text{ square inches} \][/tex]
2. Now, take half of this result to find the area:
[tex]\[ \frac{1}{2} \times 663 = 331.5 \text{ square inches} \][/tex]
3. Finally, round the result to the nearest square inch:
[tex]\[ 331.5 \approx 332 \text{ square inches} \][/tex]
Therefore, the area of the octagon, rounded to the nearest square inch, is [tex]\(332 \text{ square inches}\)[/tex].
Among the given options, the correct answer is [tex]\(332 \text{ in}^2\)[/tex].
