The trend observed about atomic radii based on the placements of elements on the periodic table is that atomic radii generally decrease from left to right across a period and increase from top to bottom within a group. This trend is primarily due to the increase in the number of protons and electrons in the nucleus as you move across a period, which increases the attractive forces and pulls the electrons closer to the nucleus, resulting in a smaller atomic radius. On the other hand, moving down a group, the number of energy levels or shells increases, leading to a larger atomic radius due to the shielding effect, where the inner electron shells reduce the attractive forces of the nucleus on the outermost electrons.
