If `D` is a point on the side `A B` of ` A B C` such that `A D : D B=3:2` and `E` is a point on `B C` such that `D E A C` . Find the ratio of areas of ` A B C` and ` B D E` .

If D is a point on the side A B of /_\ A B C such that A D : D B=3:2 and E is a point on B C such that DE||AC . Find the ratio of areas of /_\ A B C and /_\ B D E .

If A B C ∼ D E F such that A B=1. 2 c m and D E=1. 4 c m . Find the ratio of areas of A B C and D E F .

In A B C ,\ D and E are the mid-points of A B and A C respectively. Find the ratio of the areas of A D E and A B C .

A B C is a triangle. D is a point on A B such that AD=1/4A B\ a n d\ E is a point on A C such that A E=1/4A C . Prove that D E=1/4B C

A B C is a triangle. D is a point on A B such that D=1/4A B\ a n d\ E is a point on A C such that A E=1/4A Cdot Prove that D E=1/4B C

A B C D is a parallelogram. E is a point on B A such that B E=2\ E A\ a n d\ F is a point on D C such that D F=2\ F C . Prove that A E C F is a parallelogram whose area is one third of the area of parallelogram A B C D .

A B C D is a parallelogram, G is the point on A B such that A G=2\ G B ,\ E\ is a point of D C such that C E=2D E\ a n d\ F is the point of B C such that B F=2F Cdot Prove that: a r\ (\ E B G)=a r\ (\ E F C)

In Figure, A D=A E\ a n d\ D\ a n d\ E are points on B C such that B D=E Cdot Prove that A B=A C

A B C D is a parallelogram. E is a point on B A such that B E=2\ E A\ a n d\ F is a point on D C such that D F=2\ F Cdot Prove that A E\ C F is a parallelogram whose area is one third of the area of parallelogram A B\ C Ddot

If D ,\ E and F are the mid-points of the sides of a /_\A B C , the ratio of the areas of the triangles D E F and ABC is .......