In ΔABC, a line parallel to side BC cuts the side AB and AC at points D and E respectively and also point D divide AB in the ratio of 1 : 4. If area of ΔABC is 200 cm$$^{2}$$, then what is the area (in cm$$^{2}$$) of quadrilateral DECB?

The ratio of AD and DB = 1: 4 (given)

Hence, the ratio of AD and AB can be taken as 1 : 5

$$\triangle$$ ADE, $$\triangle$$ ABC are similar triangles, so their areas will be in the ratio of 1 : 25 ($$\because$$ AD : AB = 1 : 5)

Total area of the triangle = 200 

25x = 200 (or) x = 8 cm$$^{2}$$

Now, Area of ADE = 8 cm$$^{2}$$ and Area of DECB = 200 -  8 = 192 cm$$^{2}$$

Hence, option A is the correct answer.