Final answer:
To find the side length of the hexagon we use the area formula A = (3√3/2)s^2 and solve for s with the given area of 40 in^2. The solution yields a side length of approximately 4.6 inches.
Step-by-step explanation:
The question asks how to find the side length of a regular hexagon given its area. The formula for the area of a regular hexagon is A = (3√3/2)s^2 where A is the area and s is the side length. Plugging the area (40 in^2) into the formula and solving for s will give the length of a side. By rearranging the formula to solve for s, we get s = √((2A)/(3√3)). Substituting 40 in^2 for A gives us s ≈ 4.6 inches. Therefore, the correct answer is (a) 4.6 inches to the nearest tenth.