# 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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