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10. The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see Fig.). Find the area of the shaded region. (Use\pi = 3.14 and \sqrt3 = 1.73205)

                                            

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Area of an equilateral triangle is:- 

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

                                                     \frac{\sqrt{3}}{4}\times a^2\ =\ 17320.5

                                                                 a\ =\ 200\ cm

Now, consider the sector  :- Angle of sector is 60o and radius is 100 cm.

 Thus the area of the sector:-   

                                                      =\ \frac{60^{\circ}}{360^{\circ}}\times \pi \times 100^2

                                                    =\ \frac{15700}{3}\ cm^2

Thus the area of the shaded region is : 

                                                       =\ 17320.5\ -\ 3\times \frac{15700}{3}

                                                       =\ 1620.5\ cm^2 

Posted by

Devendra Khairwa

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