There is trapezium ABCD
• AE is perpendicular to DC
• BF is perpendicular to DC
• lines are drawn through point A to C, B to D , A to F , B to E.
• Those lines intersect at varius points in the figure
The description of figure is given in case of need to redraw it
The question is how many triangles are being made inside the figure
Also is there any quick way to find,calculate or count them?
Note that it is a hexagon and all vertices are connected by edges (though some lie atop each other and don't count as triangles, due to not satisfying $a+b>c$ for all cyclic shifts of edge lengths). The number of triangles in a connected graph on $n$ nodes are the number of ordered $3$-tuples from it, $n\choose3$, so in this case ${6\choose3}=20$. Then note that of these, the ${4\choose3}=4$ $3$-tuples from the $4$ vertices $C,D,E,F$ are excluded, so there are $20-4=16$ triangles.