`A B C` is a triangle in which `D` is the mid-point of `B C ,\ E\ a n d\ F` are mid-points of `D C\ a n d\ A E` respectively. If area of ` A B C` is `16\ c m^2,` find the area of ` D E F`

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A D . Prove that area of B E D = 1/4 area of ABC.

In a A B C ,\ E\ a n d\ F are the mid-points of A C\ a n d\ A B respectively. The altitude A P to B C intersects F E\ at Q . Prove that A Q=Q P .

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A Ddot Prove that area of B E D=1/4a r e aof A B Cdot

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 .

In square A B C D ,\ P\ a n d\ Q are mid-point of A B\ a n d\ C D respectively. If A B=8c m\ a n d\ P Q\ a n d\ B D intersect at O , then find area of O P B

D ,\ E ,\ F are the mid-points of the sides B C ,\ C A and A B respectively of a Delta A B C . Determine the ratio of the areas of D E F and A B C .

A B C is an isosceles triangle in which A B=A C . If D\ a n d\ E are the mid-points of A B\ a n d\ A C respectively, Prove that the points B ,\ C ,\ D\ a n d\ E are concyclic.

A B C D is a parallelogram and E is the mid-point of B C ,\ D E\ a n d\ A B when produced meet at F . Then A F=

A B C D is a square. F is the mid-point of A Bdot B E is one third of B C . If the area of F B E=108\ c m^2 , find the length of A C .

A B C is a triangle in which D is the mid-point of BC and E is the mid-point of A D . Prove that area of triangle B E D=1/4area \ of triangle A B C . GIVEN : A triangle A B C ,D is the mid-point of B C and E is the mid-point of the median A D . TO PROVE : a r( triangle B E D)=1/4a r(triangle A B C)dot