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A doorway is decorated as shown in the figure. There are four semi-circles. BC, the diameter of the larger semi-circle is of length 84 cm. Centres of the three equal semi-circles lie on BC. ABC is an isosceles triangle with AB = AC. If BO = OC, find the area of the shaded region. begin mathsize 12px style open parentheses T a k e space straight pi equals 22 over 7 close parentheses end style



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Asked by Topperlearning User 7th June 2016, 8:27 AM
Answered by Expert
Answer:

H e r e comma space r a d i u s space o f space l a r g e r space s e m i space c i r c l e space equals 84 over 2 equals 42 space c m
A n d comma space r a d i u s space o f space s m a l l e r space s e m i space c i r c l e equals fraction numerator 84 over denominator 3 cross times 2 end fraction equals 14 space c m
A r e a space o f space t h e space s h a d e d space r e g i o n
equals fraction numerator straight pi open parentheses 42 close parentheses squared over denominator 2 end fraction plus 3 cross times fraction numerator straight pi open parentheses 14 close parentheses squared over denominator 2 end fraction minus 1 half cross times 84 cross times 42
equals 22 over 7 space left square bracket 21 cross times 42 space plus space 3 cross times 14 cross times space 7 right square bracket space minus space 42 cross times 42
equals 22 space left square bracket 3 cross times 42 space plus space 42 right square bracket space minus space 42 cross times space 42
equals 42 open square brackets 66 plus 22 minus 42 close square brackets
equals 42 cross times 46
equals 1932 space c m squared


Answered by Expert 7th June 2016, 10:27 AM
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