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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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best_answer

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

Thus area of quadrant:-  

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

                                                =\ 628\ cm^2

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

Area of shaded region is :     =\ 628\ -\ 400\ =\ 228\ cm^2 

Posted by

Devendra Khairwa

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