Bars, Rods, Cylinders, Prisms, Columns...
The bars, rods, cylinders, prisms, columns, and such herein ; are all with regular polygons and the circle, right angle cross sections.
I start with all these figures having their end faces at right angles to the main body. As examples shown in Fig.-26.
This web page is going to be very simple. I only have one important item to stress!
The Center-line is only where I measure the length or height of these type of figures!
The reason will be more apparent in the web pages coming next. But, for openers: if I took a straight slice through any figure choice shown above, at a 45 degree angle, and then moved further down the figure for another 45 degree slice, but in the opposite direction__ the surface area of the new middle object, excluding the ends, may still be calculated with simple multiplication of the Center-line times the right cross sectional Area. The end cross sections would be rectangles for the square bar, and ellipses for the round circular column. When slicing these objects as such, the outside is no longer equal to the center-line. (With the exception of plane cuts being parallel, and forming a side view parallelogram.)
The logic for doing this is: Why teach a math formula, that applies for one object or a few, and then when that object has done a proportionate change, it requires different math formulation? Especially when one single type formula will handle a multitude of figures.