Question

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. [CBSE 2017]

Answer 1

We have,
Side of square = 28 cm and radius of each circle = $\frac{28}{2}$ cm


Area of the shaded region

= Area of the square + Area of the two circles − Area of the two quadrants

$$\begin{gathered} ={\left(28\right)}^2+2\times \mathrm{\pi }\times {\left(\frac{28}{2}\right)}^2-2\times \frac{1}{4}\times \mathrm{\pi }\times {\left(\frac{28}{2}\right)}^2 \\ ={\left(28\right)}^2+\frac{3}{2}\times \mathrm{\pi }\times {\left(\frac{28}{2}\right)}^2 \\ ={\left(28\right)}^2\left(1+\frac{3}{2}\times \frac{22}{7}\times \frac{1}{2}\times \frac{1}{2}\right) \\ ={\left(28\right)}^2\left(1+\frac{33}{28}\right) \\ ={\left(28\right)}^2\times \frac{61}{28} \\ =28\times 61 \\ =1708{\mathrm{cm}}^2 \end{gathered}$$

Therefore, the area of the shaded region is 1708 cm².