trapezium, how to calculate angles?

Question

I like to draw the following picture:

It is generated with following code:

    \documentclass[12pt,tikz,border=3mm]{standalone}
    %    \usepackage{zfc-book-standalone}
    \usetikzlibrary{arrows.meta,positioning,shapes}
    %---------------------------------------------------------------%
            \begin{document}
    \begin{tikzpicture}[
    node distance = 0mm and 0mm,
L/.style = {line width=1mm, draw=gray,
            arrows={-Stealth[fill=gray,inset=0pt,length=0pt 1.2,angle'=90]},
            },
T/.style 2 args = {name=n#1,
                   draw=#2, fill=#2!20,% draw and fill color
            trapezium, 
            trapezium stretches body,
            trapezium left angle=105, trapezium right angle=75,
            inner sep=0mm, outer sep=0mm, 
            text width=33mm, text height=4mm,
            rotate=-15,
                   }
                        ]
%-------- 
\node[T={1}{teal}]                          {}  (0,0); 
\node[T={2}{teal},  below right=of n1.bottom left corner,
            anchor=top left corner]  {};
\node[T={3}{teal},  below right=of n2.bottom left corner,
            anchor=top left corner]  {};
%-------- 
\node[T={4}{cyan},  trapezium left angle=75, trapezium right angle=105,
            text height=3mm, %text width=33mm + 2.8977/2 mm,
            rotate=30,
            below left =of n3.bottom right corner,
            anchor=top right corner]         {};
%-------- 
    \foreach \i [count=\xi from 4]  in {5,6,7}
\node[T={\i}{teal},below right=of n\xi.bottom left corner,
            anchor=top left corner]  {};
%-------- 
    \foreach \i in {1,2,...,7}
\draw[L,shorten <=11mm,shorten >=11mm]    
            \ifnum\i=4
(n4.east) -- (n4.west)
            \else
(n\i.west) -- (n\i.east)
            \fi;          
%--------
\draw[red,ultra thin]   (n1.top  left corner) |- (n7.bottom  left corner)
                        (n1.top right corner) |- (n7.bottom right corner);
%----------------
    \end{tikzpicture}
            \end{document}

I read all relevant questions here, but didn't find solution, hot to determine angles in trapezium such that left shapes border will be aligned (see discrepancy pointed out with red line on the left of stack).

Questions: Is there a way, beside guessing, to determine left and right trapezium for given rotate angle, trapezium width and height in such a way, that left (and right) shape borders are aligned, i.e. lie on vertical line?

Edit: After reading again Drawing parallelogram with fixed angle, width and height?, as suggest 'percusse' I realise, that if I change in above MWE minimum width and height with fixed measures obtained by text width and text height, I solve most of problems:

Still open is the following question:

How to determine text width, that it will be independent from text height?

Answer 1

Why not just draw this directly? This gives:

and the code is even simpler:

\documentclass[12pt,tikz,border=3mm]{standalone}
\usetikzlibrary{arrows.meta,positioning,shapes}
\begin{document}

\begin{tikzpicture}[scale=0.5,T/.style={draw=#1,fill=#1!20},
      L/.style = {line width=1mm, draw=gray,
                  arrows={-Stealth[fill=gray,inset=0pt,length=0pt 1.2,angle'=90]}}]
   \draw[T=teal](0,10)--(8,9)--(8,6)--(0,7)--cycle;
   \draw[T=cyan](8,6)--(8,5)--(0,4)--(0,5)--cycle;
   \draw[T=teal](0,4)--(8,3)--(8,0)--(0,1)--cycle;
   \foreach \ht in {9,8,3,2} {
     \draw[teal] (0,\ht)--++(8,-1);
   }
   \foreach \ht in {1.25,2.25,3.25,7.25,8.25,9.25} {
      \draw[L](2,\ht)--++(4,-0.5);
   }
   \draw[L](6,5.25)--++(-4,-0.5);
   \draw[step=5mm] (0,0) grid (10);

   \draw[red](0,0)--(0,10);% for comparing the LHS
\end{tikzpicture}

\end{document}

Of course, if this is part of something more general then this might not be appropriate...and perhaps I have made poor guesses for your dimensions, but it looks close to what you want for your MWE.

In terms of "trapeziums with general angles", I would use the calc library to compute and then plot the corresponding coordinates in the same way.