Question

The two triangular prisms shown are similar. The dimensions of the larger prism were multiplied by a scale factor of to create the smaller prism.


When the large prism was reduced, the surface area changed by a factor of

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Answer 1

If the linear scale factor is k, surface areas scale by k^2. So the surface area changed by a factor of k^2.

(For example, if the prism was reduced by a factor of 2/3, the surface area changes by (2/3)^2 = 4/9.)