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  • The area of an equilateral triangle ABC is 17320.5 cm 2 . 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.

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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