Given DE || BC, AD = 1 cm and DB = 2 cm.

So, AB = 3 cm.

In ΔABC and ΔADE,

∠ABC = ∠ADE [corresponding angles]

∠ACB = ∠AED [corresponding angles]

∠A = ∠A [common angle]

We know that AAA similarity criterion states that in two triangles, if corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.

∴ ΔABC ~ ΔADE

We know that the ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

∴ ar (ΔABC): ar (ΔADE) = 9: 1