Final answer:
To find the surface area of a regular hexagonal prism, calculate the area of the base using the formula for the area of a regular hexagon. Then, find the lateral surface area using the formula for the lateral surface area of a rectangular prism. Finally, add the areas together to find the total surface area.
Step-by-step explanation:
To find the surface area of a regular hexagonal prism, we first need to find the area of the hexagon base. The formula for the area of a regular hexagon is A = (3√3/2) * s^2, where s is the length of one side of the hexagon. In this case, the side length is 3.5 cm. So the area of the base is A = (3√3/2) * (3.5)^2 = 0.095 (rounded to three decimal places).
Next, we need to find the lateral surface area of the prism. Since a hexagonal prism has six faces, each face is a rectangle with one side equal to the side length of the hexagon base and the other side equal to the height of the prism. The formula for the lateral surface area of a rectangular prism is A = 2 * l * w, where l is the length and w is the width of the rectangle. In this case, the length is the side length of the hexagon base, 3.5 cm, and the width is the height of the prism, 11 cm. So the lateral surface area of the prism is A = 2 * 3.5 * 11 = 77 cm^2.
Finally, we can find the total surface area by adding the area of the base and the lateral surface area: Total Surface Area = Base Area + Lateral Surface Area = 0.095 + 77 = 77.095 cm^2 (rounded to three decimal places).