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CBSE Class 10 Answered

In fig. APB and AQO are semicircles, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region.
Asked by Abha | 14 Feb, 2016, 02:35: PM
answered-by-expert Expert Answer
In space the space given space figure space there space are space two space semicircles space APB space and space AQO. APB space is space having space OB space as space redius. AQO space is space having space AO space as space diameter. Given space that space AO space equals space OB Let space AO space equals space straight r space equals space OB Perimeter space of space the space shaded space region space equals space circumference space of space semicircle space space APB space plus space circumference space of space semicircle space space AQO 40 space equals space πr space plus straight pi straight r over 2 80 equals 3 πr straight r space equals space fraction numerator 80 over denominator 3 straight pi end fraction space cm.............. left parenthesis 1 right parenthesis Area space of space shaded space region space equals space Area space of space semicircle space space APB space plus space Area space of space semicircle space space AQO equals space πr squared space plus straight pi open parentheses straight r over 2 close parentheses squared equals space fraction numerator 5 πr squared space over denominator 4 end fraction equals fraction numerator 5 straight pi open parentheses fraction numerator 80 over denominator 3 straight pi end fraction close parentheses squared space over denominator 4 end fraction........... left parenthesis from space left parenthesis 1 right parenthesis right parenthesis equals fraction numerator 5 cross times 80 cross times 80 over denominator 9 straight pi cross times 4 end fraction equals 283.09 cm squared Area space of space shaded space region space is space 283.09 cm squared.
Answered by Vijaykumar Wani | 15 Feb, 2016, 11:17: AM

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