To find the area of a regular hexagon using the apothem and the side length, we can use the formula:
Area = (Perimeter × Apothem) / 2
First, we need to calculate the perimeter of the hexagon. A regular hexagon has six sides of equal length. Therefore, the perimeter (P) can be calculated as:
P = 6 × Side Length
Given the side length is 12 yards:
P = 6 × 12 = 72 yards
Next, we substitute the values into the area formula. We know the apothem is 10.4 yards:
Area = (72 × 10.4) / 2
Calculating this gives us:
Area = 748.8 / 2 = 374.4 square yards
Thus, the area of the regular hexagon is 374.4 square yards.