Two triangular prisms are similar. The perimeter of each face of one prism is double the perimeter of the corresponding face of the other prism. How are the surface areas of the figures related?

For similar figures, corresponding lengths have the same scale factor. Since the larger prism’s corresponding face perimeters are double, its linear scale factor is 2. Surface area scales by the square of the linear factor, so the ratio is 2² = 4; the larger prism has 4 times the surface area of the smaller prism.

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