Height Is Not a Side

The height is the perpendicular distance from the line of the base to the opposite vertex. A right-angle mark shows where the height meets that line. A sloping side is longer than the height, so you cannot use it in place of the height. In a right triangle, one leg can be the base and the other leg the height.

The height can land outside the base

In an obtuse triangle the height may not land on the base at all. Extend the base with a dashed line and draw the perpendicular from the vertex to the extension. That dashed perpendicular is still the height. The base is still the side itself, which is 6 here, not the extended length. The formula does not change. Only the drawing needs more care.