Question

In the given figure, DE || BC
(i) If DE = 4 cm, BC = 6 cm and Area (∆ADE) = 16 cm², find the area of ∆ABC.
(ii) If DE = 4 cm, BC = 8 cm and Area (∆ADE) = 25 cm², find the area of ∆ABC.
(iii) If DE : BC = 3 : 5. Calculate the ratio of the areas of ∆ADE and the trapezium BCED.

Answer 1

In the given figure, we have DE || BC.

In ΔADE and ΔABC

$\angle ADE=\angle B\left(\mathrm{Corresponding}\mathrm{angles}\right)$

$\angle DAE=\angle BAC\left(\mathrm{Common}\right)$

So, $∆ADE~∆ABC$ (AA Similarity)

(i) We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.

Hence

(ii) We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.

Hence,

(iii) We know that

Let Area of ΔADE = 9x sq. units and Area of ΔABC = 25x sq. units

Now,