"Height" always means vertical measurement (up and down), while "width"
often, but not always means horizontal measurement (right to left).  Sometimes 
"base" is used for the horizontal meansurement.

But when rectangles are turned sideways and the height becomes the width (base)
and the width (base) becomes the height.  But since width x height and
height x width are the same, it doesn't matter which we call which.

It is customary to label the greater dimension of a rectangle the "length" and
the shorter the "width".  But this is not always adhered to.

The best way would be to say "The area of a rectangle is the product of the
two perpendicular dimensions" and make the formula A = d1d2.

Edwin