In $$\triangle ABC, D$$ and E are points on AB and BC, respectively, such that DE is parallel to AC. If DE = 3 cm, AC = 5 cm and the area of trapezium ACED = 32 cm$$^2$$, then what will be the area of $$\triangle BDE$$?

Using AAA similarity, triangle BDE will be similar to triangle BAC.
And the sides will be in the ratio 3:5 i.e. DE : AC.
Ratio of area of triangle BDE and BAC = square of 3:5 = 9 : 25.
Let us assume that the area of triangle BAC = 25x. This means that the area of triangle BDE = 9x.
Subtracting area of BDE from the area of BAC = Area of trapezium ACED.
25x - 9x = 32
x = 2.
This gives the area of triangle BDE = 9x = 18 sq. cm.