Solution:-

From the question it is given that,

DE || BC, DE = 6 cm, BC = 9 cm and area of ∆ADE = 28 sq. cm

From the fig, ∠D = ∠B and ∠E = ∠C … [corresponding angles are equal]

Now consider the ∆ADE and ∆ABC,

∠A = ∠A … [common angles for both triangles]

Therefore, ∆ADE ~ ∆ABC

Then, area of ∆ADE/area of ∆ABC = (DE)²/(BC)²

28/area of ∆ABC = (6)²/(9)²

28/area of ∆ABC = 36/81

area of ∆ABC = (28 × 81)/36

area of ∆ABC = 2268/36

area of ∆ABC = 63 cm²