To find the area of a regular hexagon, you can use the formula:
Area = (Perimeter × Apothem) / 2
First, we need to calculate the perimeter of the hexagon. A regular hexagon has six equal sides, so the perimeter (P) can be calculated as:
P = 6 × Side length
Given that the side length is 12 yards, the perimeter would be:
P = 6 × 12 = 72 yards
Now that we have the perimeter, we can use it in our area formula along with the given apothem length of 10.4 yards:
Area = (72 × 10.4) / 2
Calculating this gives:
Area = (748.8) / 2 = 374.4 square yards
Therefore, the area of the regular hexagon with an apothem of 10.4 yards and a side length of 12 yards is 374.4 square yards.