Answer:
Part A) The surface area of prism B is equal to the surface area of prism A multiplied by the scale factor (m) squared
Part B) The Volume of prism B is equal to the Volume of prism A multiplied by the scale factor (m) elevated to the cube
Step-by-step explanation:
Part A) we know that
The scale factor is equal to m
The surface area of the prism is equal to

where
B is the area of the base
P is the perimeter of the base
h is the height of the prism
we have
Prism A



substitute
![SA=[2(xy)+2(x+y)z]\ units^{2}](https://tex.z-dn.net/?f=SA%3D%5B2%28xy%29%2B2%28x%2By%29z%5D%5C%20units%5E%7B2%7D)
Prism B



substitute
![SB=[2(xym^{2})+2m(x+y)mz]\ units^{2}](https://tex.z-dn.net/?f=SB%3D%5B2%28xym%5E%7B2%7D%29%2B2m%28x%2By%29mz%5D%5C%20units%5E%7B2%7D)
![SB=[2(xym^{2})+2m^{2}(x+y)z]\ units^{2}](https://tex.z-dn.net/?f=SB%3D%5B2%28xym%5E%7B2%7D%29%2B2m%5E%7B2%7D%28x%2By%29z%5D%5C%20units%5E%7B2%7D)
therefore
The surface area of prism B is equal to the surface area of prism A multiplied by the scale factor (m) squared
Part B) we know that
The volume of the prism is equal to

where
B is the area of the base
h is the height of the prism
we have
Prism A


substitute
![VA=[(xyz]\ units^{3}](https://tex.z-dn.net/?f=VA%3D%5B%28xyz%5D%5C%20units%5E%7B3%7D)
Prism B


substitute
![VB=[(xym^{2})mz]\ units^{3}](https://tex.z-dn.net/?f=VB%3D%5B%28xym%5E%7B2%7D%29mz%5D%5C%20units%5E%7B3%7D)
![VB=[(xyzm^{3})]\ units^{3}](https://tex.z-dn.net/?f=VB%3D%5B%28xyzm%5E%7B3%7D%29%5D%5C%20units%5E%7B3%7D)
therefore
The Volume of prism B is equal to the Volume of prism A multiplied by the scale factor (m) elevated to the cube