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)

2
by keerthanach
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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

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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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