Biggest circle inside a triangle with sides 16, 16, 24

Find the area of the largest circle that fits inside the triangle whose sides measure $16$, $16$ and $24$.

$\tfrac{144\pi}{7}$. The largest such circle is the incircle, with radius $r=\text{Area}/s$. The altitude to the long side is $4\sqrt7$, so the area is $48\sqrt7$ and $s=28$, giving $r=\tfrac{12}{\sqrt7}$ and area $\pi r^2=\tfrac{144\pi}{7}$.