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

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|