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?

The ratiOS of areas are the squares of the ratio of lengths (and the ratio of volumes are cubes of the ratio of lengths).

As the perimeter of the second is twice the perimeter of the first, each length of the second is twice the length of the first, and so the ratio of the lengths is 1:2

Thus the ratio of the areas is 1²:2² = 1:4.

Therefore the surface area of the larger prism is four times that of the smaller prism.