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CBSE Class 10 Answered

ABCD is a square of side 4cm. if E is a point in the interior of the square such that triangle CED is equilateral, then area of traiangle ACE
Asked by sankalpsamiti | 07 Feb, 2016, 01:08: AM
answered-by-expert Expert Answer
 
Join space FE. increment CED space is space equilateral space triangle CE space equals ED space equals CD space equals 4 space cm height space equals space fraction numerator square root of 3 over denominator 2 end fraction cross times 4 equals 2 square root of 3 space cm FE space equals space 4 minus 2 square root of 3 AF space equals space 1 half cross times AB space equals space 2 cm In space increment AFE space using space Pythaoras space theorem comma AF squared plus FE squared equals AE squared AE squared space equals 4 plus 16 plus 12 minus 16 square root of 3 AE squared space equals 32 minus 16 square root of 3 AE equals 4 square root of open parentheses 2 minus square root of 3 close parentheses end root AC space is space diametre space equals space 4 square root of 2 space cm In space space increment A E C straight s equals fraction numerator 4 square root of open parentheses 2 minus square root of 3 close parentheses end root plus 4 plus 4 square root of 2 over denominator 2 end fraction equals 2 square root of open parentheses 2 minus square root of 3 close parentheses end root plus 2 plus 2 square root of 2 Area space of space increment A E C equals square root of straight s open parentheses straight s minus straight a close parentheses open parentheses straight s minus straight b close parentheses open parentheses straight s minus straight c close parentheses end root equals square root of open parentheses 2 square root of open parentheses 2 minus square root of 3 close parentheses end root plus 2 plus 2 square root of 2 close parentheses open parentheses negative 2 square root of open parentheses 2 minus square root of 3 close parentheses end root plus 2 plus 2 square root of 2 close parentheses open parentheses 2 square root of open parentheses 2 minus square root of 3 close parentheses end root minus 2 plus 2 square root of 2 close parentheses open parentheses 2 square root of open parentheses 2 minus square root of 3 close parentheses end root plus 2 minus 2 square root of 2 close parentheses end root equals 4 open parentheses square root of 3 minus 1 close parentheses space cm squared
Answered by Vijaykumar Wani | 09 Feb, 2016, 10:18: AM

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CBSE 10 - Maths
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