Final answer:
Trigonal planar molecules are polar when the central atom has one lone pair, as this introduces asymmetry. Other options either preserve symmetry or describe shapes that are not trigonal planar. Polarities arise due to uneven distribution of electron density causing a permanent dipole moment.
Step-by-step explanation:
To determine when trigonal planar shapes are polar, it's essential to consider the presence of lone pairs on the central atom. The presence of lone pairs can create asymmetry in the molecular geometry which can lead to polarity.
Option A indicates no lone pairs on the central atom, producing a symmetrical shape which can be considered non-polar if all the surrounding atoms are identical. Option C suggests two lone pairs, which would no longer be a trigonal planar shape, but is related to the octahedral electron-pair geometry, specifically a square planar molecular structure when the central atom has two lone pairs in an octahedral array.
Option D, which presents three lone pairs on the central atom, describes an electron arrangement more akin to the trigonal bipyramidal geometry with lone pairs potentially occupying the equatorial positions for minimization of repulsion.
However, option B, indicating one lone pair on the central atom, typically causes a trigonal planar geometry to become bent or V-shaped due to the space taken by the lone pair and the asymmetry it introduces, which can lead to a polar molecule if the surrounding atoms are not identical.