To calculate the area of a regular hexagon when given the perimeter, we first need to break down the steps.
1. **Determine the side length of the hexagon**: A regular hexagon has six equal sides. To find the length of one side, we divide the perimeter by the number of sides. In this case, the perimeter is 48 inches.
Side length = Perimeter / Number of sides
Side length = 48 inches / 6 = 8 inches
2. **Use the area formula for a regular hexagon**: The area (A) of a regular hexagon can be calculated using the formula:
A = (3√3 / 2) × s²
where ‘s’ is the length of a side.
3. **Calculate the area**: Now that we have the side length, we can plug it into the area formula.
A = (3√3 / 2) × (8 inches)²
A = (3√3 / 2) × 64
A = (3√3 / 2) × 64 ≈ 166.28 square inches
So, the area of a regular hexagon with a 48 inch perimeter is approximately 166.28 square inches.