In the diagram $□ A B C D$ is the rectangular paper. If $A B = 20 c m$ and $B C = 14 c m$ then what is the area of the shaded region if the semicircle with diameter $B C$ is cut from the paper.

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Solution

$\begin{matrix} F r o m t h e f i g u r e R a d i u s o f s e m i - c i r c l e = \frac{14}{2} = 7 c m A r e a o f t h e s h a d e d r e g i o n = a r e a o f r e c tan e - a r e a o f s e m i c i r c l e = l e n g t h \times b r e a d t h - \frac{π r^{2}}{2} = 20 \times 14 - \frac{22}{7} \times \frac{7 \times 7}{2} = 280 - 77 = 203 c m^{2} H e n c e, a r e a o f s h a d e d r e g i o n i s 203 c m^{2} . \end{matrix}$

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