Finding Triangles in a Square

All horizontal and vertical adjacent points are at a distance \(1\text{ cm}\) each. If the number of triangles of area \(1\text{ cm}^2\) formed by using these points is \(\mu \), evaluate \(\left\lfloor \dfrac { \mu }{ 8 } \right\rfloor \).

Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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