Question

the two triangular prisms shown are similar. the dimensions of the larger prism were multiplied by a scale factor of $\frac{4}{5}$ to create the smaller prism. when the large prism was reduced, the surface area changed by a factor of $\frac{64}{125}$ $\frac{16}{25}$ $\frac{4}{5}$ $\frac{10}{8}$

Explanation:

Step1: Recall surface - area ratio formula

For similar solids, if the scale factor of the side - lengths is $k$, the ratio of the surface areas of the two similar solids is $k^{2}$.

Step2: Identify the scale factor

The scale factor $k=\frac{4}{5}$ as the larger prism's dimensions are multiplied by $\frac{4}{5}$ to get the smaller prism.

Step3: Calculate the ratio of surface areas

We square the scale factor. So, $k^{2}=(\frac{4}{5})^{2}=\frac{16}{25}$.

Answer:

$\frac{16}{25}$