The addition of a seventh above the root to a triad is so common that there is some justification for discussing these as chords in their own right.
Five different types of seventh chord can be constructed based on the diatonic triads of the major and minor scales with the addition of the seventh. These are shown in the example below, but the various types are discussed in more detail in the diatonic short progressions section.
The five types are:
You can find out the closest position (and therefore the root) of any chord by rearranging it as a stack of thirds. The following example shows a seventh chord in inversion and then rearranged in root and close position: