This shape strikes me as redundant, allowing for chord inversions to take place. The third of a chord, without getting too technical, can be found one string up and one fret down from the root note for a major chord, or one string up and two frets down for a minor chord. These are intervals of four or three frets respectively. So, to get these inverted chord shapes, we can lift up our index finger and take out the lower C, and use that finger to play a third. Therefore, a major inverted chord looks like this: Major
E String - 8 - C - Root A String - 10 - G - Fifth D String - 10 - C - Root one octave up
If this were a chord played in the "piano" voicing, it would read C (root) E (third) G (fifth). But such a shape is uncomfortable for a lot of guitar chords, whereas this inverted shape, with the G (fifth) as the lowest note, is very grounded and stable physically. Pianists refer to this as the "second inversion" or "6/4 chord," while guitarists typically call it C/G (C-over-G), because it's a C chord with the G note on the bottom. Following the principles established so far, we need only "flatten" the third of the chord (lower it one semitone, a.k.a. one fret), to get a minor equivalent. So, a C minor chord looks like this:
A String - 10 - G - Fifth D String - 10 - C - Root G String - 9 - E - Third
This is referred to as a Cm/G (C-minor-over-G) because, again, it's a C minor with the G on the bottom. If a major chord is made minor by flattening (lowering by one fret) the third, we can give it an even darker sound by making it diminished, flattening the fifth as well. This looks like:
A String - 10 - G - Fifth D String - 10 - C - Root G String - 8 - Eb - Flattened Third
This is a Cdim/G (C-diminished-over-Gb). For one last shape, the last type of triad (three-note chord) we can play, we take a major chord and raise (by one fret) the fifth. This is called an augmented chord.
A String - 9 - Gb - Flattened Fifth D String - 10 - C - Root G String - 8 - Eb - Flattened Third
This last chord is called a Caug/G# (C-augmented-over-G#). I hope you guys find this lesson on chord inversions useful, and can use this knowledge of chord construction to get away from simply memorizing chord shapes.
A String - 11 - G#/Ab - Fifth D String - 10 - C - Root G String - 9 - E - Third