Final answer:
The area of Shape B is 272 cm² since it is 4 times longer than Shape A, and thus its size transformation is by a factor of 4², making the area 16 times greater.
Step-by-step explanation:
The question seems to suggest that there's a relationship between the sizes of two shapes and their areas, implying a form of size transformation. In geometry, if one shape is a scaled version of another, the ratio of their areas is equal to the square of the ratio of their corresponding lengths. Let's apply this principle to the given problem.
If Shape A is 3 cm (presumably in one dimension, since we typically don't say that a shape itself is '3 cm') and has an area of 17 cm², and given that Shape B is 4 times longer than Shape A (since 12 cm is 4 times 3 cm), if they are similar shapes (meaning their dimensions increase proportionally), the area of Shape B would be 4² (or 16) times greater than that of Shape A. We calculate this as follows:
Area of Shape B = 4² × 17 cm² = 16 × 17 cm² = 272 cm²
Therefore, the area of Shape B would be 272 cm².