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` .

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 .

In a A B C , D a n d E are points on the sides A B and A C respectively. For each of the following cases show that D E B C : A B=12 c m , A D=8 c m , A E=12 c m a n d A C=18 c m . (ii) A B=5. 6 c m , A D=1. 4 c m , A C=7. 2 c m a n d A E=1. 8 cm

In Figure, triangle A B C is right-angled at Bdot Give that A B=9C M ,\ A C=15 C M ,\ a n d\ D ,\ E\ are the mid-points of the sides A B\ a n d\ A C respectively, calculate The length of B C (ii) The area of A D E

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 Qdot Prove that A Q=Q P

ABC is an isosceles triangle in which AB=AC. If D and E are the mid-points of AB and AC respectively,prove that the points B,C,D and E are concylic.

ABC is an isosceles triangle in which AB=AC. If D and E are the mid-points of AB and AC respectively,prove that the points B,C,D and E are concyclic.

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)

In a A B C , D and E are points on A B and A C respectively such that D E// B C . If A D=2. 4 c m ,\ \ A E=3. 2 c m ,\ \ D E=2c m and B C=5c m , find B D and C E .

In Fig. 32, A B C D is a rectangle of length A B=40\ c m and breadth B C=25\ c mdot If P , Q , R , S be the mid-points of the sides A B ,\ B C ,\ C D\ and \ D A respectively, find the area of the shaded region.