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In Fig., a circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of the inscribed circle and the area of the shaded region. [Use π = 3.14 and 3 = 1.732]
Asked by Akash Jp | 13 Mar, 2015, 07:05: PM
answered-by-expert Expert Answer

I n space a n space e q u i l a t e r a l space t r i a n g l e comma space c e n t r o i d space a n d space i n c e n t e r space i s space s a m e. H e i g h t space o f space t h e space t r i a n g l e space equals space square root of 12 squared minus 6 squared end root equals square root of 144 minus 36 end root equals square root of 108 equals 6 square root of 3 c m A O equals space O C equals 2 over 3 cross times 6 square root of 3 equals 4 square root of 3 c m R a d i u s space o f space t h e space c i r c l e space equals space square root of O C squared minus open parentheses fraction numerator B C over denominator 2 end fraction close parentheses squared end root equals square root of left parenthesis 4 square root of 3 right parenthesis squared minus open parentheses 12 over 2 close parentheses squared end root equals square root of 48 minus 36 end root equals 2 square root of 3 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 space equals fraction numerator square root of 3 over denominator 4 end fraction a squared minus πr squared equals fraction numerator square root of 3 over denominator 4 end fraction cross times 12 squared minus 3.14 cross times open parentheses 2 square root of 3 close parentheses squared equals 36 square root of 3 minus 37.68 equals 62.352 minus 37.68 equals 24.67 space cm squared

Answered by | 16 Mar, 2015, 06:15: PM

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