Q8 of 31 Page 1

Find the perimeter of the shaded region if ABCD is a square of side 21 cm and

APB & CPD are semicircles. (Use π=22/7).


Given


Side of square, a = 21 cm


Diameter of both semicircles, d = 21 cm


Let the radius of semicircle be ‘r’, then


Diameter, d = 2r


Formula used


Perimeter of semicircle = πr


Where ‘r’ is radius


Perimeter of shaded region:


= Perimeter of semicircle CPD – CD + Perimeter of semicircle APB – AB + AD + BC


= πr – 21 + πr – 21 + 21 + 21


= 2πr


= πd [∵ d = 2r]



= 66 cm


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