two triangular prisms are similar. the perimeter of each face of one prism is double the perimeter of the…

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 surface areas are the same. the surface area of the larger prism is 2 times the surface area of the smaller prism. the surface area of the larger prism is 4 times the surface area of the smaller prism. the surface area of the larger prism is 8 times the surface area of the smaller prism.

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 surface areas are the same. the surface area of the larger prism is 2 times the surface area of the smaller prism. the surface area of the larger prism is 4 times the surface area of the smaller prism. the surface area of the larger prism is 8 times the surface area of the smaller prism.

Answer

Explanation:

Step1: Recall the ratio - of - perimeters and scale factor

If the perimeter of each face of one prism is double the perimeter of the corresponding face of the other prism, the scale factor (k) of the two similar triangular prisms is (k = 2).

Step2: Recall the relationship between scale factor and surface - area

For two similar solids, if the scale factor is (k), the ratio of their surface areas (S_1) and (S_2) is given by (\frac{S_1}{S_2}=k^{2}). Since (k = 2), then (\frac{S_{larger}}{S_{smaller}}=k^{2}=2^{2}=4). So (S_{larger}=4S_{smaller}).

Answer:

The surface area of the larger prism is 4 times the surface area of the smaller prism.