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  • In Fig, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

9.  In Fig, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

                                                

Answers (1)

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Firstly, area of the smaller circle is :  

                                                               =\ \pi r^2

                                                             =\ \pi \times \left ( \frac{7}{2} \right )^2

                                                             =\ \frac{77}{2}\ cm^2

Now, area of \Delta ABC :- 

                                                  =\ \frac{1}{2}\times AB\times OC

or                                              =\ \frac{1}{2}\times 14\times 7\ =\ 49\ cm^2

And, area of the bigger semicircle is :     

                                                                 =\ \frac{1}{2}\pi r^2

                                                                =\ \frac{1}{2}\pi \times 7^2

                                                                 =\ 77\ cm^2

Hence area of shaded region is :-    

                                                           =\ \frac{77}{2}\ +\ 77\ -\ 49

                                                         =\ 66.5\ cm^2

Therefore area of shaded region is 66.5 cm2. 

Posted by

Devendra Khairwa

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