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  • In Fig, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use pi = 3.14)

13. In Fig, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use \pi = 3.14)

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In the given figure we need to find the radius of the circle:-  

Consider \DeltaOAB,

OB^2\ =\ OA^2\ +\ AB^2                                     

=\ 20^2\ +\ 20^2                                             

OB\ =\ 20\sqrt{2}\ cm

This area of the quadrant:-  

=\ \frac{90^{\circ}}{360^{\circ}}\times 3.14\times (20\sqrt{2})^2

=\ 628\ cm^2                                               

Also, the area of the square =\ 20^2\ =\ 400\ cm^2

The area of shaded region =\ 628\ -\ 400\ =\ 228\ cm^2 

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Devendra Khairwa

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