In the figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region.



Asked by Topperlearning User | 27th Jul, 2017, 02:33: PM

Expert Answer:

 begin mathsize 12px style Radius space of space the space circle space equals space OB space equals space square root of OA squared space plus space AB squared end root equals square root of 20 squared space plus space 20 squared end root
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 20 square root of 2 space cm
The space required space area space equals space Area space of space quadrant space OPBQ space minus space Area space of space square space OABC
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1 fourth straight pi space open parentheses OB close parentheses squared space minus space open parentheses OA close parentheses squared
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1 fourth space open parentheses 3.14 close parentheses space open parentheses 20 square root of 2 close parentheses squared space minus space open parentheses 20 close parentheses squared
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 228 space cm squared
Hence comma space area space of space shaded space region space equals space 228 space cm squared space end style

Answered by  | 27th Jul, 2017, 04:33: PM

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