Question

In Fig. 4.178, DE || BC

(i) If DE = 4 cm, BC = 6 cm and Area (ΔADE) = 16 cm², find the area of ΔABC.
(ii) If DE = 4cm, BC = 8 cm and Area (ΔADE) = 25 cm², find the area of ΔABC.
(iii)If DE : BC = 3 : 5. Calculate the ratio of the areas of ΔADE and the trapezium

Answer 1

We have, DE || BC, DE = 4 cm, BC = 6 cm and area (Δ) = 16cm²
In ΔADE and ΔABC
∠A = ∠A [Common]
∠ADE = ∠ABC             [Corresponding angles]
Then, ΔADE ~ ΔABC   [By AA similarity]

By area of similar triangle theorem