I Need No Corners (Count 'em All 13!)

Discrete Mathematics Level 5

The figure above shows a \(6\times5\) grid but this time with all 4 corners cut off forming triangles.

Count the total number of quadrilaterals in the grid above.

Clarification: A quadrilateral is a polygon that has 4 sides.

This is one part of Quadrilatorics.

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