Surfer can add the geometry created by the Measure Tool directly to the existing map as a new base layer, or, it can be added to an existing base layer. To do so, complete the following steps:

1. Click Map Tools | Map Tools | Measure 
2. Draw the desired line or polygon and press ENTER when finished
3. In the Measure dialog, click Options | Save Geometry to Base Layer
4. In the Destination Layer dialog, pick an existing layer, or, type in a new layer name and press OK.

Saving the measurement geometry to a Base Layer in Surfer. 

Updated October 15, 2021