VTMO 2026 - Grade 6 - Semifinal - SET 1 - Self-study Question 7

In parallelogram $ABCD$, $E$ lies on $AB$ and $F$ lies on $CD$, with $AE=\frac23AB$ and $CF=\frac23CD$. As shown, $H=AC\cap DE$ and $K=AC\cap DB$. The area of $ABCD$ is $600\text{ cm}^2$. Find the area of triangle $FHK$, in $\text{cm}^2$.