In the given figure, two squares of sides 8 cm and 20 cm are given. What is the area (in cm²) of the shaded part?

Solution (By Examveda Team)

$$\eqalign{ & \Delta DHC \sim \Delta DFG \cr & {\text{So, }}\frac{{DC}}{{DG}} = \frac{{CH}}{{FG}} \cr & \Rightarrow \frac{8}{{28}} = \frac{{CH}}{{20}} \cr & \Rightarrow CH = \frac{{40}}{7} \cr & {\text{So, area of }}\Delta DCH \cr & = \frac{1}{2} \times DC \times CH \cr & = \frac{1}{2} \times 8 \times \frac{{40}}{7} \cr & = \frac{{160}}{7}{\text{ c}}{{\text{m}}^2} \cr} $$