Taking it to the next level

Discrete Mathematics Level pending

In triangle, find the sum of the total number of triangles(excluding degenerate triangles) and quadrilaterals(excluding degenerate quadrilaterals) in the given figure.

Note: \(IJ\) and \(LK\) are perpendicular to \(AB\).

Line segment FH is parallel to AB.
G is a point on the other side of FILH compared to AB
There are 30 additional points on the line segment IL, which are connected to both A and B with line segments.
There are 27 additional points on the line segment FG, which are connected to H with line segments
There are 27 additional points on the line segment GH, which are connected to F with the line segments.

Line segment EC is parallel to AB.
D is a point on the other side of EJKC compared to AB
There are 30 additional points on the line segment EC, which are connected to both A and B with line segments.
There are 27 additional points on the line segment ED, which are connected to C with line segments
There are 27 additional points on the line segment CD, which are connected to E with line segments.

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