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.

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

= ${28}^2+2\times \pi \times (\frac{28}{2}{)}^2-2\times \frac{1}{4}\times \pi \times (\frac{28}{2}{)}^2$

= ${28}^2(1+\frac{3}{2}\times \pi \times (\frac{28}{2}{)}^2$)

= ${28}^2(1+\frac{3}{2}\times \frac{22}{7}\times \frac{1}{2}\times \frac{1}{2}$)

=${28}^2(\frac{61}{28}$)
= 28 × 61
= 1708 $c{m}^2$

Therefore, the area of the shaded region is 1708 cm²