$15 A B C$ is a right-angled triangle with $\angle B A C=90^{\circ}$. A square is constructed on the side $A B$ and $B C$ as shown. The area of the square $A B D E$ is $8 \mathrm{~cm}^{2}$ and the area of the square $B C F G$ is $26 \mathrm{~cm}^{2}$. Find the area of triangle $D B G$ in $\mathrm{cm}^{2}$.
15 Answer: (6)
We rotate $\triangle B A C 90^{\circ}$ anticlockwise about the point $B$ to get $\triangle B C^{\prime} G$. $C^{\prime} G=B C=\sqrt{26-8}=\sqrt{18}$.
$\therefore$ The area of $\triangle D B G=\frac{1}{2} \times D B \times C^{\prime} G=\frac{1}{2} \sqrt{8} \sqrt{18}=6 \mathrm{~cm}^{2}$.