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ICSE Class 9 Answered

Find the area of the quadrilateral ABCD shown in the figure given below:
Asked by Topperlearning User | 29 Aug, 2017, 12:28: PM
answered-by-expert Expert Answer

begin mathsize 12px style In space increment ABD comma straight S equals fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction equals fraction numerator 6 plus 4 plus 8 over denominator 2 end fraction equals 9 space cm Area space of space increment ABD equals square root of straight S open parentheses straight S minus straight a close parentheses open parentheses straight S minus straight b close parentheses left parenthesis straight S minus straight c right parenthesis end root equals square root of 9 open parentheses 9 minus 6 close parentheses open parentheses 9 minus 4 close parentheses open parentheses 9 minus 8 close parentheses end root equals square root of 135 space sq. space cm equals 11.62 space sq. space cm In space increment BCD comma straight S equals fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction equals fraction numerator 8 plus 7 plus 9 over denominator 2 end fraction equals 12 space cm Area space of space increment BCD equals square root of straight S open parentheses straight S minus straight a close parentheses open parentheses straight S minus straight b close parentheses left parenthesis straight S minus straight c right parenthesis end root equals square root of 12 open parentheses 12 minus 8 close parentheses open parentheses 12 minus 7 close parentheses open parentheses 12 minus 9 close parentheses end root equals square root of 720 equals 26.83 space sq. space cm Area space of space quadrilateral space ABCD equals Area space of space increment ABD plus Area space of space increment BCD equals 11.62 plus 26.83 equals 38.45 space sq. space cm end style

Answered by | 29 Aug, 2017, 02:28: PM

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