In Fig. 1,

In ∆ ADE and ∆ ABC

∠ ADE = ∠ ABC (Corresponding angles)

∠ DAE = ∠ BAC (same angle)

By AA similarity criteria which states that if two triangles have two pairs of congruent angles, then the triangles are similar.

∆ ADE ≈ ∆ ABC

We know that if two triangles are similar then the ratio of their areas is equal to the square of alternating sides.

The ratio of the ar(∆ ABC) to the ar(∆ ADE)

Ratio of the ar(∆ ABC) to the ar(∆ ADE) = 9 : 1