Question

A square OPQR is inscribed in a quadrant OAQB of a circle. If the radius of a circle is 6root2 cm find the area of the shaded region.??

Answer 1

Answer is 20.54 $cm^2$

Step-by-step explanation:

As per figure,  

• Diagonal of the quadrant = radius = $6\sqrt 2\ cm$

$side \times \sqrt 2 = 6\sqrt 2\ cm$

or Side = 6 cm

• Area of Square = $(Side)^2$

= $(6\ cm)^$2

= $36\ cm^2$

• Area of Quadrant $(\frac {1}{4})^{th}$ of the Circle = $\frac {1}{4} \times \pi r^2$

= $\frac {1}{4} \times \frac {22}{7} \times 6\sqrt 2 \times 6\sqrt 2$

= 56.54 $cm^2$

• Area of Shaded Region = Area of Quadrant - Area of Square

= 56.54 - 36

= 20.54 $cm^2$