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  • In Fig, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

15. In Fig, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

                                                           

Answers (1)

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Consider \Delta ABC,

                                          BC^2\ =\ AC^2\ +\ AB^2

                                                    =\ 14^2\ +\ 14^2

                                           BC\ =\ 14\sqrt{2}\ cm

Area of triangle is :

                                         =\ \frac{1}{2}\times 14\times 14

                                        =\ 98\ cm^2         

Now, area of sector is :  

                                            =\ \frac{90^{\circ}}{360^{\circ}}\times \pi \times 14^2

                                          =\ 154\ cm^2

And area of semicircle is  : - 

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

                                         =\ \frac{1}{2} \pi \times (7\sqrt{2})^2

                                         =\ 154\ cm^2

Hence the area of the shaded region is :     =\ 154\ -\ (154\ -\ 98)\ =\ 98\ cm^2 

Posted by

Devendra Khairwa

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