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\documentclass[tikz, border=2pt]{standalone}
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\usetikzlibrary{calc}
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\usetikzlibrary{math}
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\begin{document}
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\begin{tikzpicture}[line width=1pt]
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\tikzmath{
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\a = 13; \b = 19; \c = sqrt(\a*\a + \b*\b);
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\l = 5;
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\A = acos(\b / \c);
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\B = acos(\a / \c);
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}
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\def\template#1; {
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\draw #1 rectangle ++(\l, \l);
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\draw[rounded corners=0.01mm] #1 ++(\l, \l) -- +(180-\A:\b/\c*\l) -- +(-\l, 0) -- cycle;
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\draw[rotate around={\B:($#1 + (0, \l)$)}] ($#1 + (0, \l)$) rectangle +(\a/\c*\l, \a/\c*\l);
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\draw[rotate around={90-\A:($#1 + (\l, \l)$)}] ($#1 + (\l, \l)$) rectangle +(\b/\c*\l, \b/\c*\l);
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}
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\template{(0, 0)};
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\coordinate (O1) at (0, 0);
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\coordinate (A1) at ($(O1)+(0, \l)$);
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\coordinate (B1) at ($(O1)+(\l, \l)$);
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\filldraw[rotate around={\B:(A1)}, fill=gray, draw=black] (A1) rectangle +(\a/\c*\l, \a/\c*\l);
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\filldraw[rotate around={90-\A:(B1)}, fill=gray, draw=black] (B1) rectangle +(\b/\c*\l, \b/\c*\l);
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\def\trans#1#2#3; {
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\coordinate (O) at #1;
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\coordinate (A) at ($({180-\A}:{(\a+\b)/\c*\l}) + (O) + (\l, \l)$);
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\coordinate (B) at ($(\B:{(\a+\b)/\c*\l}) + (O) + (0, \l)$);
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\coordinate (C) at ($(\B:{\b/\c*\l}) + (A)$);
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\coordinate (D) at ($(-\A:{\a/\c*\l}) + (A)$);
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\draw[dashed, rounded corners=0.01mm] (A) -- (C) -- (B);
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\filldraw[fill=gray, draw=black, rounded corners=0.01mm] ($(O) + (0, \l)$) -- (D) -- ($(\B:{#2*\b/\c*\l}) + (A)$) -- ($({\B-180}:{(\a-#2*\b)/\c*\l}) + (A)$) -- cycle;
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\filldraw[fill=gray, draw=black, rounded corners=0.01mm] ($(O) + (\l, \l)$) -- (D) -- ($({180-\A}:{#3*\a/\c*\l}) + (B)$) -- ($({-\A}:{(\b-#3*\a)/\c*\l}) + (B)$) -- cycle;
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}
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\trans{(10, 0)}{0.4}{0.6};
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\template{(10, 0)};
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\trans{(20, 0)}{1}{1};
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\template{(20, 0)};
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\coordinate (O4) at (5, -12);
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\coordinate (A4) at ($(\B:{\a/\c*\l}) + (O4)$);
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\filldraw[fill=gray, draw=black, rounded corners=0.01mm] (O4) -- (A4) -- ($(O4) + (\l, 0)$) -- ++(0, \l) -- ($(A4) + (0, \l)$) -- ($(O4) + (0, \l)$) -- cycle;
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\template{(5, -12)};
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\coordinate (O5) at (15, -12);
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\filldraw[fill=gray, draw=black] (O5) rectangle +(5, 5);
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\template{(15, -12)};
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\end{tikzpicture}
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\end{document}
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