Geometry

Question Analysis  
This problem involves two similar hexagonal prisms with a given scale factor.
We are provided with the lateral surface area and base area of the smaller prism and asked to find the total surface area of the larger prism.  

Key Concept Explanation  
1. Hexagonal Prism Surface Area:  
  A hexagonal prism has two hexagonal bases and six rectangular lateral faces.  
  Total Surface Area (SA) = Lateral Surface Area + 2 × Base Area.  
2. Scaling in Similar Prisms:  
   If two prisms are similar, their corresponding linear dimensions (e.g., side lengths, heights) are proportional.  
  Areas (lateral surface area, base area) scale with the square of the linear scale factor.  
     

Step-by-Step Solution  
1. Given Data for Smaller Prism:  
  Lateral Surface Area () = 120 cm²  
  Base Area () = 15 cm²  
  Total Surface Area () = Lateral SA + 2 × Base Area