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

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

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 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

P is any point on base B C of A B C\ a n d\ D is the mid-point of B CdotD E is drawn parallel to P A to meet A C at Edot If a r\ ( A B C)=12 c m^2 , then find area of E P C

A B C D is a parallelogram in which B C is produced to E such that C E=B C. A E intersects C D\ at F . Prove that a r\ (\ A D F)=\ a r\ (\ E C F) . If the area of \ D F B=3\ c m^2, find the area of ABCD.

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=

If ΔA B C ∼ ΔD E F such that area of ΔA B C is 9\ c m^2 and the area of ΔD E F is 16\ c m^2 and B C=2. 1 cm. Find the length of E F .

In Figure, A B C D isa trapezium in which side A B is a parallel to side D C and E is the mid-point of side A Ddot If F is a point on the side B C such that the segment E F is parallel to side D C . Prove that F is the mid point of B C and E F=1/2(A B+D C)dot

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