Final answer:
To calculate the surface area of a hexagonal prism, we need to add the lateral area to the area of the two hexagonal bases. The surface area is approximately 1430.44 cm².
Step-by-step explanation:
To calculate the surface area of a hexagonal prism, we need to add the lateral area to the area of the two hexagonal bases. In this case, the lateral area is given as 432 cm². Since a hexagonal prism has six rectangular faces, each face has an area of 432 ÷ 6 = 72 cm². The area of a hexagonal base is given by the formula A = 3 √3 × s², where s is the length of a side. Since the hexagon has six sides, the total area of the two bases is 2 × (3 √3 × s²). The surface area is then 2 × (3 √3 × s²) + 6 × 72. Plugging in the values, we get:
Surface area = 2 × (3 √3 × s²) + 6 × 72 = 2 × (3 √3 × 9²) + 6 × 72 = 2 × (3 √3 × 81) + 6 × 72 = 2 × (3 √3 × 81) + 432 = 6 √3 × 81 + 432 = 486 √3 + 432 ≈ 1430.44 cm².
Therefore, the surface area of the prism is approximately 1430.44 cm².