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 cm^{2}

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

= (60 + 50) * h

= 55h cm^{2}

So,

=

=

Area of trapezium DCYX = Area of trapezium ABXY

Rate this question :