1.1: Area in a rectangle using trigonometry

Figure 2 shows a rectangle $\displaystyle ABCD$ with $\displaystyle AB=10\,\mathrm{cm}$ and $\displaystyle AD=15\,\mathrm{cm}$. $\displaystyle E$ is the point inside the rectangle such that $\displaystyle DE=13\,\mathrm{cm}$ and $\displaystyle \angle BAE=35^\circ$.

Given that $\displaystyle \angle AED$ is obtuse, find the area, in $\displaystyle \mathrm{cm}^2$ to one decimal place, of triangle $\displaystyle BCE$.