Definition:Base of Geometric Figure
The base of a geometric figure is a specific part of that figure which is distinguished from the remainder of that figure and placed (actually or figuratively) at the bottom of a depiction or visualisation.
In some cases the base is truly qualitiatively different from the rest of the figure.
In other cases the base is selected arbitrarily as one of several parts of the figure which may equally well be so chosen.
It is immaterial which is so chosen.
In the above diagram, $AB$ is the base of the highlighted segment.
The solid figure is usually oriented so that the base is situated at the bottom.
It is usual to choose one of the bases to be the one which is conceptually on the bottom.
In the above, $ABCD$ and $EFGH$ would conventionally be identified as being the bases.
In the above diagram, $ABCDE$ is the base of the pyramid $ABCDEQ$.
Let $K$ be the right circular cone formed by the rotation of $\triangle AOB$ around $OB$.
Let $BC$ be the circle described by $B$.
In the words of Euclid: