Question

In Figure, DE || BC If DE = 4 cm, BC = 6 cm and Area (ΔADE) = 16 cm2, find the area of ΔABC.

Answer 1

We have, DE || BC, DE = 4 cm, BC = 6 cm and area (Δ𝐴𝐷𝐸) = 16 cm²

In ΔADE and ΔABC

∠A = ∠A [Common]

∠ADE = ∠ABC [Corresponding angles]

Then, ΔADE ~ ΔABC [By AA similarity]

∴ By area of similar triangle theorem

`("Area"(triangleADE))/("Area"(triangleABC))="DE"^2/"BC"^2`

`rArr16/("Area"(triangleABC))=4^2/6^2`

⇒ Area (ΔABC) = `(16xx36)/16=36"cm"^2`