Question

In the following figure, DE || BC. If DE : BC = 3 : 5. Calculate the ratio of the areas of ∆ADE and the trapezium BCED.

Answer 1

∆ADE ~ ∆ABC.

`\therefore \frac{ar(\Delta ADE)}{ar(\Delta ABC)}=(DE^2)/(BC^2)=((DE)/(BC))^2=(3/5)^2=9/25`

Let ar (∆ADE) = 9x sq units

Then, ar (∆ABC) = 25x sq units

ar (trap. BCED) = ar (∆ABC) – ar (∆ADE)

= (25x – 9x) = (16x) sq units

`\therefore \frac{ar(\Delta ADE)}{ar(trap.BCED)}=\frac{9x}{16x}=\frac{9}{16}`