CEOMETRY What is the area of a regular heptagon with a side length of 8 in . and an apothem of 8.3 in.? Round to the nearest whole number. \( 2232 \mathrm{in.}^{2} \)

To find the area of a regular heptagon (a seven-sided polygon) with a given side length and apothem, you can use the following formula: \[ \text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} \] Let's break down the steps: 1. **Calculate the Perimeter:** The perimeter \( P \) of a regular heptagon with side length \( s \) is: \[ P = 7 \times s = 7 \times 8\ \text{in} = 56\ \text{in} \] 2. **Use the Area Formula:** With the apothem \( a = 8.3\ \text{in} \), plug the values into the area formula: \[ \text{Area} = \frac{1}{2} \times 56\ \text{in} \times 8.3\ \text{in} = 28 \times 8.3\ \text{in}^2 = 232.4\ \text{in}^2 \] 3. **Round to the Nearest Whole Number:** \[ \text{Area} \approx 232\ \text{in}^2 \] **Conclusion:** The area of the regular heptagon is approximately **232 square inches**. It seems there might have been a miscalculation in your initial answer of \( 2232\ \text{in}^2 \). The correct area, based on the given measurements, is **232 square inches**.