In general, there is no relationship between the two.
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There is no relationship.
Consider a rectangle - such as a window. You can have a tall thin window, a short wide one or any shape between the two.
The height of the base is part of the triangle and the height of the prism is the height of the rectangle
V= 1/3(B x h) or one third times the area of the base times the height. The base might be a circle, square, rectangle or any polygon.
The base of a prism can be any polygon, but the polygon face parallel to the base must be congruent. True
Designate one of the faces as the base, and the distance between the plane the base is on, and the plane the opposite side is on, as the height. Then the volume is the base times the height.
A cylinder is a polygon that has circles as its base. A triangular pyramid is a polygon that has a triangle as its base.