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  • In Fig, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

9.  In Fig, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

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Firstly, the area of the smaller circle  =\ \pi r^2

=\ \pi \times \left ( \frac{7}{2} \right )^2

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

Now, the area of \Delta ABC =\ \frac{1}{2}\times AB\times OC

=\ \frac{1}{2}\times 14\times 7\ =\ 49\ cm^2

And, The area of the bigger semicircle  =\ \frac{1}{2}\pi r^2

=\ \frac{1}{2}\pi \times 7^2

=\ 77\ cm^2

Hence the area of the shaded region =\ \frac{77}{2}\ +\ 77\ -\ 49

=\ 66.5\ cm^2

Therefore the area of the shaded region is 66.5 cm2. 

Posted by

Devendra Khairwa

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