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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.

 

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

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

Thus the area of sector =\ \frac{90^{\circ}}{360^{\circ}}\times \pi (7)^2

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

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

Hence the area of the shaded region =\ 196\ -\ 4\times \frac{77}{2}  

=\ 42\ cm^2

Posted by

Devendra Khairwa

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