<s>[INST] What will be area of shaded region, in two rectangles, where 2 vertex are common? In a figure, there are two rectangles $ABCD$ and $DEBG$, each of lengh $7\ cm$ and width $3\ cm$. The area of shaded region. in $cm^2$ is approximately ? 

Options given : $12$, $10$, $8$, $4$
 [/INST] 
Here, notice that $\Delta DEK$ and $\Delta BCK$ are congruent. If we find $|DK|$, we are done. By Pythagoras Theorem, $(7-a)^2 = a^2+9 \implies a = \frac{20}{7}$. Therefore, $|DK| = 7-\frac{20}{7} = \frac{29}{7}$ and shaded area is $3 \cdot \frac{29}{7} = \frac{87}{7} \approx12$.
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