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CBSE Class 9 Answered

find the area of a quadrilateral abcd in which ab=3cm,bc=4cm,cd=4cm ,da=5cm and ac=5cm.please solve the value of the answer step by step(6+2square root of 21)
Asked by itishreepanda999 | 08 Jun, 2018, 02:45: PM
answered-by-expert Expert Answer
begin mathsize 16px style Here comma space Area space of space Quadrilateral space ABCD thin space equals space Area space left parenthesis increment ABC right parenthesis space plus space Area space left parenthesis increment ADC right parenthesis By space Heron apostrophe straight s space Formula comma Area space of space straight a space triagle space equals space square root of straight s left parenthesis straight s space minus space straight a right parenthesis space left parenthesis straight s space minus space straight b right parenthesis space left parenthesis space straight s space minus space straight c right parenthesis end root straight s equals space fraction numerator space straight a space plus space straight b space plus space straight c over denominator 2 end fraction Area space of space space increment ABC space equals space square root of space 6 left parenthesis 6 space minus space 3 right parenthesis space left parenthesis 6 space minus space 4 right parenthesis space left parenthesis space 6 space minus space 4 right parenthesis end root space space space space space space left parenthesis space since comma space straight s space equals space fraction numerator 3 space plus space 4 space plus space 5 over denominator 2 end fraction space equals space space 12 over 2 space space space equals space 6 space right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space square root of 6 space cross times space 3 space cross times 2 space cross times space 1 end root space equals square root of 6 cross times 6 end root space equals space 6 cm squared..... left parenthesis 1 right parenthesis Area space of space space increment ADC space equals space square root of space 7 left parenthesis 7 space minus space 5 right parenthesis space left parenthesis 7 space minus space 5 right parenthesis space left parenthesis space 7 space minus space 4 right parenthesis end root space space space space space space left parenthesis space since comma space straight s space equals space fraction numerator 5 space plus space 5 space plus space 4 over denominator 2 end fraction space equals space space 14 over 2 space space space equals space 7 space right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space square root of 7 space cross times space 2 space cross times space 2 cross times 3 end root space equals square root of 4 space cross times space 21 end root space equals 2 square root of space 21 end root cm squared space space....... left parenthesis 2 right parenthesis Since comma space Area space of space Quadrilateral space ABCD thin space equals space Area space left parenthesis increment ABC right parenthesis space plus space Area space left parenthesis increment ADC right parenthesis space equals space left parenthesis 6 space plus space 2 square root of space 21 end root right parenthesis cm squared space......... from space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis end style
Answered by Yasmeen Khan | 09 Jun, 2018, 12:48: PM
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