UKMT Senior Mathematical Challenge, 2022

The diagram shows a square, $KLMN$. A second square $PQRS$ is drawn inside it, as shown in the diagram, where $P$ divides the side $KL$ in the ratio $1:2$. Similarly, a third square $TUVW$ is drawn inside $PQRS$ with $T$ dividing $PQ$ in the ratio $1:2$. What fraction of the area of $KLMN$ is shaded?

(A) $\frac{25}{81}$ (B) $\frac{16}{49}$ (C) $\frac{4}{9}$ (D) $\frac{40}{81}$ (E) $\frac{2}{3}$