It is 'Half an hour'.
In English Grammar, any noun, prefixed by the indefinite article, that begins , with a,e,i,o,u & h uses 'AN'.
e.g. An Horse, An House,
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A half of an hour is 30 min. and hour and a half is 90 min.
40 minutes is what hour
no days just half an hour
Ninety minutes are in an hour and a half
A half hour is equal to 30 minutes.