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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?

Verified Answer :

AL2006


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.

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