Marked with white is the area A* has to eplore before finding the path marked with red. It starts from the north, desperately exploring that peninsula, but as it turns out to be a dead-end, it then has to go into all directions until finally finding a way around that bay on the nort-west corner of the lake area.

It is moments like these which really show the incredible computing power of human perceptory system. For a human eye it is immediately self-evident that exploring to the east and north is inefficient because there won't be a way around in those dircetions. But a computer has no way of knowing it, unless it scans the map pixel by pixel...