Taking it to the next level

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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