VTMO 2026 - Grade 9 - Semifinal - SET 07 - Self-study Question 4

Triangle $ABC$ is right isosceles at $A$, with $AB=6$cm. Points $M\in AB,N\in AC$ satisfy $AM=4$cm,$AN=2$cm. Points $P,Q\in BC$ satisfy $PM\perp MN$ and $QN\perp MN$. Find the area of $MNQP$ in square centimeters.