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ICSE Class 9 Answered

One side of a ||gm is 50 cm. The diagonals are 68 cm and 48 cm. Find the area of the ||gm.
Asked by Topperlearning User | 29 Aug, 2017, 12:14: PM
answered-by-expert Expert Answer

begin mathsize 12px style Area space of space parallelogram space ABCD equals 4 cross times area space of space increment AOB
In space increment AOB comma
AO equals 1 half AC equals 1 half cross times 68 equals 34 space cm
BO equals 1 half BD equals 1 half cross times 48 equals 24 space cm
straight S equals fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction equals fraction numerator 34 plus 24 plus 50 over denominator 2 end fraction equals 54 space cm
Area space of space increment AOB 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 54 open parentheses 54 minus 34 close parentheses open parentheses 54 minus 24 close parentheses open parentheses 54 minus 50 close parentheses end root
equals square root of 129600
equals 360 space sq. space cm
area space of space parallelogram equals 4 cross times 360 equals 1440 space sq. space cm
end style

Answered by | 29 Aug, 2017, 02:14: PM
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