What is there to explain? A planar molecule has all of the atoms in the same plane. A nonplanar one does not.
Explanations for why benzene is one type and cyclohexane the other can be found at
http://in.answers.yahoo.com/question/index?qid=20090817022032AAT8Zax
It has to do with what kind of carbon bonds are formed.
Benzene and cyclohexane molecules both contain six-membered rings. Benzene is a planar molecule, and cyclohexane is nonplanar. Explain.
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