question_answer

In the given figure, ABCD is a rectangle of dimensions \[21\,cm\times 14\text{ }cm\]. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure.

Answer:

Area of shaded region

= Area of rectangle \[\] Area of semi circle

\[=l\times b-\frac{1}{2}\pi {{r}^{2}}\]

\[=21\times 14-\frac{1}{2}\times \frac{22}{7}\times 7\times 7\]

\[=294-77\]

\[=217\,\,c{{m}^{2}}\]

Perimeter of shaded region \[=2l+b+\pi r\]

\[=2\times 21+14+\frac{22}{7}\times 7\]

\[=42+14+22\]

\[=78\,\,cm\]