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atul bhardwaj Grade:
        

ABCD is a parallelogarm. M is the mid point of side BC. a line is draw  AM which cut the BD at O. find the  area of quadilateral OMCD

6 years ago

Answers : (1)

Pramod J AskiitiansExpert-IIT-B
36 Points
										

Dear student,


triangle AOD and OMB are similar since all angles are same


BM=1/2*AD => DO:OB = 2:1


=> BO = 1/3*BD and we know vector BD is sum of vectors of BA,AD


so area of triangle OBM = (1/2)*|BO X BM|


BM = BC/2


Area of quad OMCD = area of triangle BCD - area of triangle OBM


 area of triangle BCD = (1/2)|AB X AD|


=> Area of quad OMCD = (1/2)|AB X AD| - (1/2)*(1/6)|(BA+AD) X BC|
=> Area of quad OMCD = (1/2)|AB X BC| - (1/2)*(1/6)|(BC-AB) X BC|


6 years ago
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