What do you call the empty/arid zones on both sides of a highway?

I'm referring to something like the brown areas in this picture:

Solution 1:

The edge of the road (as others have mentioned) is the shoulder.

Beyond the shoulder is the verge.

The whole strip of land the road follows is called a right-of-way in some places and a reserve in other places.

Solution 2:

The answer to your question largely depends upon the context.

If you mean the land on which the highway passes through, this is known as a right of way. Essentially, it is land granted for passage of highways and railways. And, typically the zone of the right of way extends quite a bit on either side of the roadway.

If you are referring to the waste area (undeveloped/uninhabited land) on either side when driving through a desert, you usually will refer to this by the specific biome or flora you see. For example: salt flats, desert, cactus patch, red rock mesas, etc.

If you mean the strip of land immediately adjacent to a road, often covered in gravel, this is known as the shoulder of the road. This area is typically used for stopping at roadside, or for the passage of emergency vehicles.

Solution 3:

The berm.

Ref.: Merriam-Webster Online

berm

2 : the shoulder of a road

http://www.merriam-webster.com/dictionary/berm