question_answer

In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square where O and O? are centres of the circles. Find the area of shaded region.

Answer:

\[r=\frac{1}{2}\] (side) \[=14\text{ }cm\], \[\because \] side \[=28\text{ }cm\]

Area of shaded region \[=2\times (area\text{ }of\text{ }circle)+area\text{ }of\text{ }square-2\times (area\text{ }of\text{ }quadrant)\]

\[=2\times \pi {{r}^{2}}+{{(side)}^{2}}-2\left( \frac{1}{4}\times \pi {{r}^{2}} \right)\]

\[=2\pi {{r}^{2}}-\frac{1}{2}\pi {{r}^{2}}+{{(side)}^{2}}=\frac{3}{2}\pi {{r}^{2}}+{{(side)}^{2}}\]

\[=\frac{3}{2}\times \frac{22}{7}\times 14\times 14+28\times 28=924+784\]

\[=1708\,\,c{{m}^{2}}\]