2022 IIMC keystage2-EMIC individual Question 13

In the diagram below, $ABC$ is a triangle where $AB=AC$ and $\angle BAC=90^\circ$. Points $D$ and $E$ are on $BC$ such that $\angle DAE=45^\circ$. If $BD=5$ cm and $EC=12$ cm, then what is the area, in cm$^2$, of triangle $ABC$?