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  • Find the area of the shaded region in Fig, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.

4. Find the area of the shaded region in Fig, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.

                                                       

Answers (1)

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Area of the shaded region is given by  =   Area of triangle  +  Area of the circle  -  Area of the sector 

Area of the sector is : - 

                                                  =\ \frac{60^{\circ}}{360^{\circ}}\times \pi\times 6^2

or                                               =\ \frac{132}{7}\ cm^2

And, the area of the triangle is :

                                              =\ \frac{\sqrt{3}}{4}a^2\ =\ \frac{\sqrt{3}}{4}\times 12^2\ =\ 36\sqrt{3}\ cm^2

And, the area of the circle is : =\ \pi r^2

or                                        =\ \pi \times 6^2

or                                        =\ \frac{792}{7}\ cm^2

Hence the area of the shaded region is:- 

                                                            =\ 36\sqrt{3}\ +\ \frac{792}{7}\ -\ \frac{132}{7}

or                                                         =\ \left ( 36\sqrt{3}\ +\ \frac{660}{7} \right )\ cm^2

Posted by

Devendra Khairwa

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