Triangle in Square

Geometry Level 4

Square \(ABCD\) has side length \(5\). Points \(M\), \(N\), and \(P\) are the midpoints of \(AB\), \(BC\), and \(AD\) respectively. The area of the triangle bounded by the lines \(AN\), \(BP\), and \(DM\) can be expressed as \(\dfrac{p}{q}\) for positive coprime integers \(p\) and \(q\). Find \(p+q\).

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