Question : In $\triangle ABC$, D and E are points on the sides AB and AC, respectively, such that DE || BC and DE : BC = 6 : 7. (Area of $\triangle {ADE}$ ) : (Area of trapezium BCED) = ?

Question : In $\triangle$ABC, D and E are points on AB and AC, respectively, such that DE || BC and DE divide the $\triangle$ABC into two parts of equal areas. The ratio of AD and BD is:

Question : D, E, and F are the midpoints of the sides BC, CA, and AB, respectively of a $\triangle ABC$. Then the ratio of the areas of $\triangle DEF$ and $\triangle ABC$ is:

Question : $D$ and $E$ are points on the sides $AB$ and $AC$ respectively of $\triangle ABC$ such that $DE$ is parallel to $BC$ and $AD: DB = 4:5$, $CD$ and $BE$ intersect each other at $F$. Find the ratio of the areas of $\triangle DEF$ and $\triangle CBF$.

Question : In a triangle ABC a straight line parallel to BC intersects AB and AC at D and E, respectively. If AB = 2AD, then DE : BC is: