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.

Answer 1

we know that

if the perimeter of each face of one prism is double the perimeter of the corresponding face of the other prism and the two triangular prisms are similar

then

the scale factor is equal to



so



substitute the value of the scale factor







therefore

the answer is the option

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

Answer 2

Answer:

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

Step-by-step explanation:

It is given that the perimeter of each face of one prism is double the perimeter of the corresponding face of the other prism and the two triangular prisms are similar.

It is clear that the scale factor is $2$.

We need to determine the relation between their surface areas.

So, the surface areas will vary with the scale factor of $2^{2} =4$.

The ratio of surface areas is $1:4$.

Hence, the surface area of the larger prism is four times the surface area of the smaller prism.

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