Question

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.

Explanation:

Step1: Recall the ratio - area relationship

For similar figures, if the ratio of corresponding linear measures (such as perimeters) is \(k\), the ratio of their surface - areas is \(k^{2}\).

Step2: Identify the value of \(k\)

Given that the perimeter of each face of one prism is double the perimeter of the corresponding face of the other prism, so \(k = 2\).

Step3: Calculate the ratio of surface - areas

The ratio of the surface area of the larger prism to the surface area of the smaller prism is \(k^{2}\). Substituting \(k = 2\) into \(k^{2}\), we get \(2^{2}=4\).

Answer:

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