##”SA”=2(wl+lh+hw)##

For a rectangular prism with sides ##w,l,h##, the surface area is

##”SA”=2(wl+lh+hw)##

This occurs since there are two pairs of three different faces on every rectangular prism.

Each pair of faces is a different rectangle using two of the the three dimensions of the prism as its own side.

One side is just ##wl##, another is just ##lh##, and the other ##hw##. Since there are two of each, that is reflected in the formula by the multiplication by ##2##.

This could also be imagined as a series of flattened-out rectangles:

The blue rectangles are ##2*wl##.

The yellow rectangles are ##2*lh##.

The red rectangles are ##2*hw##.

Again, the surface area would be

##”SA”=2wl+2lh+2hw##

##=2(wl+lh+hw)##