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?

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?

Answer: Option B

Solution

Answer: Option B

Solution:

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