# Definition:Prism/Height

## Definition

The **height** of a prism is the length of the perpendicular between the bases of the prism.

In the above diagram, the distance $h$ is the **height** of the prism $AJ$.

### Euclidean variant

Although the height of a prism is generally understood to be the length of the perpendicular joining opposite faces, Euclid was inconsistent in his usage in *The Elements*.

In his Proposition $39$ of Book $\text{XI} $: Prisms of equal Height with Parallelogram and Triangle as Base, he defines the base of one prism as being one of the opposite parallel faces, but of the other he defines the base as being an arbitrary one of the parallelograms.

Having defined the base in this manner, the **height** is then defined as being the height of one of the opposite parallel faces whose base is the edge which intersects the base so defined.

Using this definition, the distance $h$ in the above diagram is the **height** of the prism $PQRSTU$.