Answer :

(i) Join DY and extend it to meet AB produced at P

BYP = CYD (Vertically opposite angles)


DCY = PBY (Since DC || AP)


BY = CY (Since Y is the mid-point of BC)


Hence, by A.S.A. congruence rule


ΔBYP ΔCYD


DY = YP


And,


DC = BP


Also,


X is the mid-point of AD


Therefore,


XY || AP


And,


XY = AP


XY = (AB + BP)


XY = (AB + DC)


XY = (60 + 40)


= × 100


= 50 cm


(ii) We have,


XY || AP


XY || AB and AB || DC


XY || DC


DCYX is a trapezium.


(iii) Since X and Y are the mid-points of AD and BC respectively


Therefore,


Trapezium DCYX and ABYX are of same height and assuming it as 'h' cm


Area (Trapezium DCYX) = (DC + XY) * h


= (40 + 50) h


= 45h cm2


Area (Trapezium ABYX) = (AB + XY) * h


= (60 + 50) * h


= 55h cm2


So,


=


=


Area of trapezium DCYX = Area of trapezium ABXY


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