Question

pls help with this question

Answer 1

Join DY and exted it to meet AB produced at P. ∠BYP = ∠CYD [Vertically opposite angles].∠DCY = ∠PBY  [Since DC || AP]. and BY = CY (Since Y is the mid-point of BC). So, according to ASA congruence criterion, we getΔBYP ≅ ΔCYD ⇒ DY = YP and DC = BPAlso, X is the mid-point of AD ∴ XY || AP and XY = ½AP ⇒ XY = ½ (AB + BP) ⇒ XY = ½ (AB + DC) ⇒ XY = ½ (50 + 30)         = ½ × 80 = 40 cm. Also, We have    XY || AP ⇒ XY || AB and AB || DC ⇒ XY || DC ⇒ DCYX is a trapezium. 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.    Ar(Trap. DCYX) = ½ (DC + XY) × h                           = ½ (30 + 40) h                           = 35h cm2

Ar(Trap. ABYX) = ½ (AB + XY) × h                        = ½ (50 + 40)h                        = 45h cm2

So, Ar(trap. DCYX) /Ar(trap. ABYX) = 35h / 45h = 7/ 9

⇒ Ar(trap. DCYX) = 7/9 Ar(trap. ABXY)