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  • In Fig, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.

7. In Fig, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.

                                                

Answers (1)

best_answer

It is clear from the figure that area of all sectors are equal (due to symmetry).

Also, the angle of sector is 90o and radius is 7 cm.

Thus area of sector is :- 

                                                      =\ \frac{90^{\circ}}{360^{\circ}}\times \pi (7)^2

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

And, the area of square is :       =\ a^2\ =\ 14^2\ =\ 196\ cm^2

Hence area of shaded region is  :        

                                                              =\ 196\ -\ 4\times \frac{77}{2}

                                                              =\ 42\ cm^2

Posted by

Devendra Khairwa

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