Fhyujk

I want to draw the dashed lines as shown in the below figure:

I have achieved the following so far:

MWE:

documentclass{article}

usepackage{tikz}

usepackage{xcolor}

usetikzlibrary{decorations.pathmorphing}

tikzset{zigzag/.style={decorate,decoration=zigzag}}

begin{document}

begin{tikzpicture}

  coordinate (c) at (0,-2);

  coordinate (d) at (4,-2);

  coordinate (e) at (2,-4);

  draw[thick,red,zigzag] (-2,0) coordinate(a) -- (2,0) coordinate(b);

  draw[thick,fill=blue!20] (c) -- (b) -- (d) -- (e) -- (c);

  draw[thick] (a) -- (c);

  draw[thick,red,dashed] (0.8,0.08) -- (0,-0.8);

end{tikzpicture}

end{document} 

The task is not so difficult with decorations.markings:

documentclass[tikz,margin=3mm]{standalone}

usetikzlibrary{decorations.pathmorphing,decorations.markings}

tikzset{zigzag/.style={decorate,decoration=zigzag}}

begin{document}

begin{tikzpicture}

coordinate (c) at (0,-2);

coordinate (d) at (4,-2);

coordinate (e) at (2,-4);

draw[thick,red,zigzag,postaction={

    decoration={

        markings,

        mark=at position 0.7 with coordinate (x);

    },

    decorate

}] (-2,0) coordinate(a) -- (2,0) coordinate(b);

draw[thick,fill=blue!20] (c) -- (b) -- (d) -- (e) -- cycle;

draw[thick,postaction={

    decoration={

        markings,

        mark=at position 0.7 with coordinate (y);

    },

    decorate

}] (a) -- (c);

draw[dashed,red,thick] (x)--(y);

end{tikzpicture}

end{document} 

Bonus

Your entire figure:

documentclass[tikz,margin=3mm]{standalone}

usepackage{mathrsfs}

usetikzlibrary{decorations.pathmorphing,decorations.markings,calc,positioning}

tikzset{zigzag/.style={decorate,decoration=zigzag}}

begin{document}

begin{tikzpicture}

coordinate (c) at (0,-2);

coordinate (d) at (4,-2);

coordinate (e) at (2,-4);

draw[thick,red,zigzag,postaction={

    decoration={

        markings,

        mark=at position 0.7 with coordinate (x);,

        mark=at position 0.5 with coordinate (singularity);

    },

    decorate

}] (-2,0) coordinate(a) -- (2,0) coordinate(b);

draw[thick,fill=blue!20] (c) -- (b) -- (d) -- (e) -- cycle;

draw[thick,postaction={

    decoration={

        markings,

        mark=at position 0.7 with coordinate (y);

    },

    decorate

}] (a) -- (c);

draw[dashed,red,thick] (x)--(y);

node[below left=1em and 1em of y,align=right,red] (es) {excision\surface};

draw[red,->] (es)--($(y)+(-.1,-.1)$);

node[above=10ex of singularity,red] (sn) {singularity};

draw[red,->] (sn)--($(singularity)+(0,1)$);

node[below left=.5ex and 2ex of b] {$mathcal{H}^+$};

path (b) -- (d) node[midway,above right] {$mathcal{I}^+$};

path (d) -- (e) node[midway,below right] {$mathcal{I}^-$};

path (e) -- (c) node[midway,below left] {$mathcal{H}^-$};

node[right=0pt of d] {$i^0$};

draw[postaction={

    decoration={

        markings,

        mark=at position 0.15 with coordinate (enblue);

    },

    decorate

},thick,blue] (d) to[out=-150,in=-30] (c);

draw[<-,thick,blue] (enblue)--($(enblue)+(-60:1)$)--($(enblue)+(-60:1)+(.2,0)$) node[right,align=left] {$t$ = constant\in Schwarzschild\coordinates};

path[postaction={

    decoration={

        markings,

        mark=at position 0.35 with coordinate (engren);

    },

    decorate

}] (c)--(b);

draw[thick,green!50!black,postaction={

    decoration={

        markings,

        mark=at position 0.6 with coordinate (enargr);

    },

    decorate

}] (d) to[out=180,in=-30] (engren);

draw[thick,dashed,green!50!black] (engren)--($(engren)+(150:0.7)$);

draw[<-,thick,green!50!black] (enargr)--($(enargr)+(60:0.75)$)--($(enargr)+(60:0.75)+(2,0)$) node[right,align=left] {$tau$ = constant\in Kerr-Schild\coordinates};

end{tikzpicture}

end{document} 

It is possible to use the intersections library which allows to calculate the intersection point of 2 paths. Here the zigzag path and the dashed path.

To draw a dashed parallel, I used the calc library.

The principle.
I kept your path draw[thick,red,dashed] (0.8,0.08) -- (0,-0.8); I shifted the starting point to the right by trial and error to find the right intersection.

I calculated the intersection named i of this path and the zigzag. Then I build a parallel path called dash through this point.

I calculate the intersection of this path with the other side (the ac side) and draw the parallel segment (i)--(l).

documentclass[tikz,border=5mm]{standalone}



%usepackage{xcolor}

usetikzlibrary{decorations.pathmorphing}

usetikzlibrary{intersections}

usetikzlibrary{calc}

tikzset{zigzag/.style={decorate,decoration=zigzag}}

begin{document}

begin{tikzpicture}

  coordinate (c) at (0,-2);

  coordinate (d) at (4,-2);

  coordinate (e) at (2,-4);

  draw[name path=zz,thick,red,zigzag] (-2,0) coordinate(a) -- (2,0) coordinate(b);

  draw[thick,fill=blue!20] (c) -- (b) -- (d) -- (e) -- (c);

  draw[thick,name path=ac] (a) -- (c);

  path[name path=trans] (.9,0.08) -- (0,-0.8);

  coordinate [name intersections={of= zz and trans,by={i}}];

  coordinate (j) at ($(i)+(c)-(b)$);

  coordinate(k) at ($(i)+(b)-(c)$);

  path[name path=dash](j)--(k);

  path[name intersections={of= ac and dash,by={l}}];

  draw [thick,red,dashed] (i) -- (l);

end{tikzpicture}

end{document} 

You can easily calculate where a point in the middle between two other points lies:

documentclass{article}

usepackage{tikz}

usepackage{xcolor}

usetikzlibrary{decorations.pathmorphing,calc}

tikzset{

    zigzag/.style={

        decorate,

        decoration={

            zigzag,

            amplitude=2.5pt,

            segment length=2.5mm

        }

    }

}

begin{document}

    defposition{0.6}

    begin{tikzpicture}[thick]

        coordinate (c) at (0,-2);

        coordinate (d) at (4,-2);

        coordinate (e) at (2,-4);

        draw[red, zigzag] (-2,0) coordinate(a) -- (2,0) coordinate(b);

        draw[fill=blue!20] (c) -- (b) -- (d) -- (e) -- (c);

        draw (a) -- (c);

        draw[red, densely dashed, shorten >=0.5pt] ($(a)!position!(c)$) -- ($(a)!position!(b)$);

    end{tikzpicture}

end{document}