Triangular King

The white chess king set out on a journey and arrived in a new country. After much wandering, he settled in a country somewhat reminiscent of his homeland. Here is a map of this country:

Here he began to wander the field, moving from one cell to another, but only if they share a common side. One day, while lodging at field $A$, he wondered what was the minimum number of moves needed to reach field $B$. Help the wandering white king solve this pseudo-chess puzzle.