If a potential third variable is a function of two others, is necessarily redundant?

#1
Say I am using regression analysis to try and estimate the assembly time for widgets (which can be produced in various sizes) given some possible independent variables:

  • Width
  • Height
  • Quantity of pieces (different sizes used as components)
  • Did the American League win the World Series
  • etc.

Most finished widgets are rectangular, however I'm wondering if the "squareness" of a widget explains some of the assembly time. That is, let's say Widget A is 2 feet wide and 18 feet long. Widget B is 6 feet square. Each have the same area (36 sq ft), but my hunch is that because of the assembly process, Widget B will take longer due to its square shape.

Now to my question...

Since "squareness" is really just a calculated ratio of two other included variables (width and height), is it already "explained" in these two variables? Is it redundant to include "squareness" or similar ratio as an independent variable?
 
#2
Re: If a potential third variable is a function of two others, is necessarily redunda

If it is theoretically interesting, and adds to the predictive value of the model does it matter if it is redundant? You will have, in all liklihood, significant multicollinearity problems if you do this.