In ΔABC, points D and E are taken on AB and AC respectively such that DE ∥ BC. It is given that AD = 4 cm, DB = 8 cm and AC = 18 cm.
(i) Prove that ΔADE is similar to ΔABC.
(ii) Using the similarity, find the lengths AE and EC.
(iii) Determine the ratio of the areas of ΔADE and ΔABC.