Geometry

Question Analysis
This question requires determining the scale factor based on the given lengths of two similar rectangular prisms and then using it to calculate the surface area of the larger prism.
The main focus is on applying the concept of similarity to find the other dimensions of the larger prism and then using the surface - area formula for a rectangular prism.

Key Concept Explanation
For similar rectangular prisms, the ratio of corresponding side lengths is the scale factor.
Once the scale factor is found, we can use it to find the other dimensions of the larger prism.
The surface area formula for a rectangular prism is , where is the length, is the width, and is the height.

Step - by - Step Solution
First, find the scale factor.
The scale factor is the ratio of the lengths of the two prisms, so .
The width of the larger prism is cm, and the height of the larger prism is cm.
Then, use the surface - area formula:

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