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

\[= \left( 28 \right)^2 + 2 \times \pi \times \left( \frac{28}{2} \right)^2 - 2 \times \frac{1}{4} \times \pi \times \left( \frac{28}{2} \right)^2 \]
\[ = \left( 28 \right)^2 + \frac{3}{2} \times \pi \times \left( \frac{28}{2} \right)^2 \]
\[ = \left( 28 \right)^2 \left( 1 + \frac{3}{2} \times \frac{22}{7} \times \frac{1}{2} \times \frac{1}{2} \right)\]
\[ = \left( 28 \right)^2 \left( 1 + \frac{33}{28} \right)\]
\[ = \left( 28 \right)^2 \times \frac{61}{28}\]
\[ = 28 \times 61\]
\[ = 1708 {cm}^2\]

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