Question

If the side length of a square pyramid is triple and the slant height is divided by 5 what would be the formula to find the modified surface area

Answer 1

If the original side length is "s" and the original slant height is "h", the original surface area is
.. S = (base area) +(lateral area)
.. S = s² +(1/2)*(4s)*h
.. S = s(s +2h)

Now, if we make these replacements: s ⇒ 3s, h ⇒ h/5, we have
.. S' = (3s)(3s +2h/5)
.. S' = 9s² +(6/5)s*h . . . . . . . the formula for the modified area (in terms of original dimensions)

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Of course, in terms of the modified dimensions, the formula is the same:
.. S' = s'(s' +2h')