In the given figure and DE : BC = 3: 5. Calculate the ratio of the areas of ΔADE and the trapezium BCED.

It is given that DE || BC

∴∠ ADE = ∠ ABC (Corresponding angles)

∠ AED = ∠ ACB (Corresponding angles)

So, by AA similarity criterion ΔADE ~ ΔABC

We know that if two triangles are similar then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.

Hence, proved.