IMSO 2017 — Mathematics — Short Answer Question 17

In the diagram below, square $AEJH$ and square $FCGL$ overlap to form the shaded square $KJIL$. The area of $KJIL$ is $\frac14$ the area of $FCGL$ and $\frac49$ the area of $AEJH$. What fraction of the square $ABCD$ is shaded?