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 `D C E` is (a) 1.1:1 (b) 1:1.1 (c) 1:1 (d) 0.9:1

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

A B C D is a square. E is the mid-point of B C and F is the mid-point of C D . The ratio of the area of triangle A E F to the area of the square A B C D is (a) 1 : 2 (b) 1 : 3 (c) 1 : 4 (d) 3 : 8

ABC and BDE are two equilateral triangles such that D is the mid-point of BC .The ratio of the areas of the triangles ABC and BDE is 2:1(b)1:2(c)4:1(d)1:4

ABCD is a rectangle and E and F are the mid-points of AD and DC respectively.Then the ratio of the areas of EDF and AEFC would be (a) 1:2 (b) 1:3 (c) 1:4 (d) 2:3

A B C D is a trapezium with parallel sides A B=a\ a n d\ D C=bdot If E\ a n d\ F are mid-points of non-parallel sides A D\ a n d\ B C respectively, then the ratio of areas of quadrilaterals A B F E\ a n d\ E F C D is: a : b (b) (a+3b):(3a+b) (3a+b):(a+3b) (d) (3a+b):(3a+b)

D ,\ E ,\ F are the mid-point of the sides B C ,\ C A\ a n d\ A B respectively of A B Cdot Then D E F is congruent to triangle. A B C (b) AEF (c) B F D ,\ C D E (d) A F E ,\ B F D ,\ C D E

If D ,E ,F are the mid-points of the sides B C ,C Aa n dA B respectively of a triangle A B C , prove by vector method that A r e aof D E F=1/4(a r e aof A B C)dot

What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of the rectangle as base and a vertex on the opposite side of the rectangle? (a) 1 : 2 (b) 2 : 1 (c) 3 : 1 (d) Data inadequate (e) None of these

D, E and F are respectively the mid-points of the sides BC, CA and AB of aDeltaA B C . Show that (i) BDEF is a parallelogram. (ii) a r" "(D E F)=1/4a r" "(A B C) (iii) a r" "(B D E F)=1/2a r" "(A B C)