If the width and height of a rectangular prism are each shrunk to one seventh of the original size but the length remains the same, what is the formula to find the modified surface area?

Hey there,

Let's say    'L'=length,  'W'=width, and  'H'=height.

The surface area of a rectangular prism is  

                         A  =  (2LW) + (2WH) + (2LH)  =  2 (LW + WH + LH)

If you shrink the width and height, then the new width is  W/7 
and the new height is H/7.

The new surface area is

                         A = (2 L W/7) + (2 W/7 H/7) + (2 L H/7) .

That's               A = 2 (LW/7 + WH/49 + LH/7) .

or you could write it as      A = 2/7 (LW + WH/7 + LH)

There are many more ways to massage the formula and write it 
in different ways, but I think writing it just that way is OK.