Final answer:
Cis-trans-[10]annulene is non-aromatic due to significant transannular strain, preventing planarity, while [14]annulene manages to retain planarity despite hydrogen repulsions, thus being aromatic.
Step-by-step explanation:
Understanding the aromaticity of compounds such as annulenes requires considering their molecular geometry, electron count, and the associated ring strain. Smaller cyclic hydrocarbons, specifically medium-sized rings with 7 to 13 carbon atoms, tend to pucker or bend to minimize angle strain but also experience transannular strain, which is the steric repulsion between groups attached to non-adjacent ring atoms, resulting in non-planar configurations that are non-aromatic. [14]annulene, however, is large enough that the flexibility of the ring enables it to adopt a planar conformation despite the hydrogen repulsions, fulfilling the requirements for aromaticity according to Huckel's rule (4n+2 π-electrons) thereby exhibiting planarity and sp² hybridization throughout the ring.
Molecules like cis-trans-[10]annulene are not aromatic primarily due to their inability to maintain a planar structure as a result of significant transannular strain. Whereas, in larger rings such as [14]annulene, even though hydrogen repulsions exist, the molecule can retain a planar shape because the ring is flexible enough to accommodate these repulsions without significant puckering, thus achieving aromatic character.