Let $x$ and $y$ be the distances shown. Then the shaded area is $8y+x$. But there are a number of similar triangles and from one pair $\frac{x}{8}=\frac{y}{1}$ i.e. $x=8y$. So,

${\displaystyle \frac{\text{shaded area}}{\text{total area}}=\frac{8y+x}{9(x+y)}=\frac{8y+8y}{9\times 9y}=\frac{16}{81}}$