You probably want to be careful with the height of your 'bar' 9"-10" is awfully high above a base cabinet, especially if you have cbts. above.
1.) most base cbts with c-top is @36" H. raised bars above should only raise @6" total giving you a total bar height of 42" that still gives you room to put electrical outlets horizontally above work surface.
2.) most bar stools are 24", 30" or 36" high. the latter being for a raised bar at 42".
3.) you might look at your plates, if you are really going to use this as on eating surface, most dinner plates are 10-12" (they're getting bigger), plus you'll have to cover the wall of 4 1/2" plus an over hang on the "work surface"side, then you'll want to comfortably cozy up to the bar, so getting you knees in there without hitting too much, you'll want at least 12" on the back side. So you might want to think about a total of a 18-20" wide top.
Good Luck

Here is a link that might be useful: granite countertops

FYI...bar-height is 6" taller than counter height, not 9-10". I don't think you'd be able to find bar stools for 9-10".

Height from finished floor:
Table-height: 30"
Counter-height: 36"
Bar-height: 42"

If you decide to go w/a raised bar, I would make the raised counter 14 - 15 inches deep, not 12". 12" really isn't that deep an area and will make it difficult to eat there w/a normal sized plate + glass. Many of today's plates are now 12" wide or more (which is one reason why more and more people are going with 14" or 15" deep upper cabinets). If your dishes happen to be larger (or even 10"), you will have to be careful not them push it over the edge while eating. That would make for an uncomfortable meal, IMO.

In the non-linked photo, the raised counter appears to be simply for display...note the plate/flatware/utensils are on the lower counter, not the upper.

I also noted there is quite a bit of overlap w/the lower counter in your linked photo. The NKBA recommended overhang (extending past the lower counter) is 12" for bar-height. So, if you have a 12" overhang then a 15" surface is easy w/the "extra" 3" overlapping the lower counter. Granted the 12" overhang is a "recommendation", but recommendations are made for a reason...

As to multi-level counters in general, there are quite a few threads discussing this....pros/cons. Personally, I don't like them as it breaks up wonderful workspace for larger projects (baking, prepping, crafts, etc.) and it can be difficult for children & older people to get into/out of the 6" higher stools. They really don't hide anything either, if that's someone's intent...any tween/teen/adult-sized person standing up will easily see over the overhang and onto the counter in front of it. And, of course, anyone sitting at the counter is looking right at the mess...regardless of seated height.

But, it's your kitchen, so it's up to you.

Thanks for the suggestions. I seem to have overlooked some basics.

We just remodeled our kitchen and had the raised bar cut down so the entire surface is now the same level. We lived with the raised bar for 14 years and I loved it. But I have to say that the one level counter is much more useful. Honestly, I would never go back to the raised bar. I have a much larger work space and lots of room to lay out and serve food when we have company!

SWMBO evidently told me that she didn't want the raised counter. He who never listens (HWNL) to SWMBO was looking for an elegant solution to a problem that didn't exist.
Thanks for the tips anyway.