Question

In Fig. 7.179, DE || BC
(i)If DE= 4 cm, BC = 6cm and Area $\left(\Delta ADE\right)=16c{m}^2$, find the area of $\Delta ABC$.
(ii) If DE =4 cm, BC = 8 cm and Area $\left(\Delta ADE\right)=25c{m}^2$, find the area of $\Delta ABC$.
(iii) If DE : BC = 3 : 5. Calculate the ratio of the areas of $\Delta ADE$ and the trapezium BCED.

Answer 1

In ΔADE and ΔABC
∠C = ∠E [DE||BC]
∠A = ∠A [common]
Then, ΔADE ~ ΔABC [By AA similarity]
(i)

(ii)

(iii)