Find the area of the shaded design in Fig. 12.17, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter. (Use π = 3.14)

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2016-03-06T13:36:13+05:30

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Let Unshaded regions be 1, 2, 3 and 4
 Area of 1 + Area of 3= Area of ABCD – Areas of two semicircles of each of radius 5 cm 
Area of 1 and 3 = ( 10 * 10 - 2 * 1/2 * 3.14 * 5 *5)  [Area of semi circle                                                                                         =  1/2  pie r²]
                          = (100 - 3.14 * 25)
                          = (100 - 78.5)
                          =21.5 cm²
So,

Even the Area of 2 and 4 is equal to 21.5cm²

So,
Area of shaded region = Area of ABCD - Area 0f( 1+2+3+4)
                                       = 100 - (21.5 + 21.5)
                                       = 100 - 43
Area of shaded region = 57cm²

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2016-03-06T15:05:35+05:30

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Let Unshaded regions be I, II, III and IV 
 Area of I + Area of III= Area of ABCD – Areas of two semicircles  
                                   = ( 10X10 - 2X1/2 X 3.14 X 5 X5)  
                                   = (100 - 3.14 * 25)
                                   =21.5 cm²


similarly Area of II and IV is equal to 21.5cm²

So,
Area of shaded region = 100 - (21.5 + 21.5)
                                     =  57cm²
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