Can't get MacBook Air to display properly on SyncMaster SA350 Samsung monitor

I just got a used SA350 Samsung Monitor. I've connected it to my MacBook Air using an HDMI cable and adapter. In the display settings, if I select "Best for Display", then the image appears really zoomed in and about 3 inches of the screen on either side are black. If I select "Scaled", then I only have two options to choose from, 1280x1024 or 800x600. But both of these options still look pretty zoomed in, (not as much as with the "Best for Display" configuration) and I still have two black sections on either side of the screen. The image below is with the 1280x1024 configuration. My MacBook Air is a 13 inch, mid 2013

1.3 GHz Intel Core i5

4 GB 1600 MHz DDR3

Intel HD Graphics 5000 1536 MB

This is what the Displays tab shows under About my Mac:

But in fact, the native resolution of the SA350 is 1920 x 1080.

Hoping someone can help me. Thanks!

Marianne