Question

A prism has the surface area of 160 square feet. If dimensions are reduced by 1/4 what is the surface area of the new prism?

Answer 1

notice the prism
it's really just 6 rectangles stacked up to each other at the corners

to find the surface area, just find the area of each individual rectangle and SUM THEM UP

notice that of all 6 rectangles, there are 3 pairs
2 rectangles are usually equal
thus 3 pairs

so one can say that the area for a pair would be 2(height * width)
for another pair would be 2(length * width)
and for the last pair would be 2(length * height)

so one can say that the Area of the prism is 2hw + 2lw + 2lh

we dunno how long each is, so let us use a regular prism, that is, all sides are the same length, let's say "x" value

if that were the case, then the Area of the prism would be 2xx + 2xx + 2xx

now, use 1/4 for each side, see what you get