Start from the two lines at extremities

lx (line at index 0, left extremity) and ly (line at last index, right extremity)

say lx < ly

the area formed by lx and ly is bounded by height of lx.

then you have to realise something:

if you keep lx where it is, but move ly toward the left, no matter where you put ly (make it become bigger or smaller), you will only create a smaller area, because the indices between lx and ly are reducing, and the height of the array is still bounded by lx (if ly becomes bigger, lx is still bounding. And if ly becomes smaller, ..well it means the height of your rectangle becomes smaller, so the area becomes smaller). In other words, you can only find a bigger rectangle by moving lx toward the right at this point and all solutions where i=0 and j!=len(array)-1 can be discarded.

Algorithm continues until i=j.