Thanks for your answer, but the shortest distance is 32.5ft.
Convert the 3-D room to 2-D by folding the long wall down so that it's level with the floor, making a rectangle 19.5' by 26'. The shortest distance is a straight line running along the diagonal across the floor meeting the long edge and running from this point to the corner (20'+12.5').
The length of the diagonal is sqrt((12+7.5)^2+26^2)=32.5ft. The same result is reached if the spider climbs at an angle across the long wall first and then crawls across the ceiling to the corner. But the distance is longer if the spider crawls across the short wall and then crosses the ceiling (sqrt((26+7.5)^2+12^2=35.58ft), because this is the diagonal of a different rectangle.
Crossing the floor diagonally then climbing to the corner (or climbing the wall vertically and crossing the ceiling diagonally) is in fact a crooked path, as can be seen in the 2-D model.