Question 25
Circle $\omega$ is inscribed in rhombus $H M_{1} M_{2} T$ so that $\omega$ is tangent to $\overline{H M_{1}}$ at $A$, $\overline{M_{1} M_{2}}$ at $I$, $\overline{M_{2} T}$ at $M$, and $\overline{T H}$ at $E$. Given that the area of $H M_{1} M_{2} T$ is $1440$ and the area of $E M T$ is $405$, find the area of $A I M E$.