How does one calculate the taper ratio of a compound wing?
Taper Ratio is a simple geometrical metric that is valid for rectangles and trapezoids. If the leading edge and/or trailing edge of the wing is bent or jagged, Taper Ratio does not have a very useful meaning anymore. The Taper Ratio of the Concord wing in the OP diagram is zero.



For the compound wing in the OP diagram, the situation is a bit ambiguous as well. Is the wing root the projection of the leading edge into the fuselage, and is the extension at the root just an aerodynamic streak that uses the structural members of the main wing? 

The definition of Mean Aerodynamic Cord uses wing root and wing tip as well, and is subject to the same complications. There are some pretty intricate graphs for wings wing a compound planform, this one is from Torenbeek.

 

If you would want to use Taper Ratio with a compound planform wing, the best average would be a weighted one, where for each of the wing planform segments the Taper Ratio and the area is determined, resulting in average TR per area.