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, the ratio of corresponding perimeters gives the scale factor for their lengths. Since one prism’s face perimeters are double the corresponding perimeters, its linear scale factor is 2. Surface area scales by the square of the linear factor, so the larger prism’s surface area is 2² = 4 times the smaller prism’s surface area.

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