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?

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03-05-2016
Mathematics

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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?

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Dontthankmebrainme Dontthankmebrainme · Answer 1 · 2016-05-03T18:51:41+02:00

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.