\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}
\usepackage{tkz-euclide}
\usetikzlibrary{angles,quotes}
\usetkzobj{all}
\usetikzlibrary{shapes, calc, decorations}
\usepackage{amsmath,amssymb}
\usepackage{helvet}
\usepackage[eulergreek]{sansmath}

\begin{document}
\begin{preview}
\begin{tikzpicture}[very thick,font=\sansmath\sffamily]
    \tkzDefPoint(0,0){A}
    \tkzDefPoint(6.4,0){B}
    \tkzDefPoint(2.5,5){C}

    \tkzLabelPoints[below left,font=\sansmath\sffamily](A)
    \tkzLabelPoints[below right,font=\sansmath\sffamily](B)
    \tkzLabelPoints[above,font=\sansmath\sffamily](C)

    % Perpendiculars
    \tkzDefLine[perpendicular=through A,/tikz/overlay](B,C)\tkzGetPoint{tmp}
    \tkzInterLL(B,C)(A,tmp)\tkzGetPoint{ha}
    \tkzLabelPoint[right,font=\sansmath\sffamily](ha){$h_a$}

    \tkzDefLine[perpendicular=through B,/tikz/overlay](A,C)\tkzGetPoint{tmp}
    \tkzInterLL(A,C)(B,tmp)\tkzGetPoint{hb}
    \tkzLabelPoint[left,font=\sansmath\sffamily](hb){$h_b$}

    \tkzDefLine[perpendicular=through C,/tikz/overlay](A,B)\tkzGetPoint{tmp}
    \tkzInterLL(A,B)(C,tmp)\tkzGetPoint{hc}
    \tkzLabelPoint[below,font=\sansmath\sffamily](hc){$h_c$}

    \tkzInterLL(B,hb)(A,ha)\tkzGetPoint{H}

    % Draw polygon
    \tkzDrawPolygon[thick,fill=gray!10](A,B,C)

    % Mark angles
    % \tkzMarkAngle[arc=l,size=0.6cm,fill=green!30](B,A,C)
    % \tkzLabelAngle[pos=0.3](B,A,C){$\alpha$}

    % \tkzMarkAngle[arc=l,size=0.6cm,fill=red!30](C,B,A)
    % \tkzLabelAngle[pos=0.4](C,B,A){$\beta$}

    % \tkzMarkAngle[arc=l,size=0.6cm,fill=blue!30](A,C,B)
    % \tkzLabelAngle[pos=0.4](A,C,B){$\gamma$}

    % Label lines
    % \tkzLabelSegment[below](A,B){$c$}
    % \tkzLabelSegment[left](A,C){$b$}
    % \tkzLabelSegment[right](B,C){$a$}

    % Draw polygon
    \tkzDrawPolygon[fill=yellow](ha,hb,hc)
    \tkzDrawSegments[dashed](A,ha B,hb C,hc)
    \tkzDrawPolygon[thick](A,B,C)
    \tkzDrawPoints[size=2,fill=black](ha,hb,hc,H)
    \tkzLabelPoint[below right,font=\sansmath\sffamily](H){$H$}

    \draw pic[semithick, draw, angle radius=3mm,"$\cdot$",angle eccentricity=.6]{angle= B--hc--C};
    \draw pic[semithick, draw, angle radius=3mm,"$\cdot$",angle eccentricity=.6]{angle= B--hb--C};
    \draw pic[semithick, draw, angle radius=3mm,"$\cdot$",angle eccentricity=.6]{angle= C--ha--A};
\end{tikzpicture}
\end{preview}
\end{document}
