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  • In Figure-9, a square OPQR is inscribed in a quadrant OAQB of a circle. If the radius of circle is  ,  find the area of the

In Figure-9, a square OPQR is inscribed in a quadrant OAQB of a circle. If the radius of circle is  6\sqrt{2} cm,  find the area of the shaded region.  

 

 

 
 
 
 
 

Answers (1)

\\\text { Radius of the circle = OQ = } 6 \sqrt{2}\mathrm{cm} \\\\ \text { Let side of the square is 'a' cm } \\ \mathrm{OP}^{2}+\mathrm{PQ}^{2}=(OQ)^{2} \\ \mathrm{a}^{2}+\mathrm{a}^{2}=(6 \sqrt{2})^{2} \\ 2a^2 = 72 \\ {a}=6 \mathrm{cm}\\ \text {Area of shaded region = Area of quardant OAQB - Area of the square OPQR} \\\\=\frac{90}{360} \times \pi r^{2} -\mathrm{a}^{2} \\\\=\frac{1}{4} \times \frac{22}{7} \times(6 \sqrt{2})^{2} -36 \\ =20.57 \ cm^2

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