Figure. represents a cuboid. The lengths of the edge, `A E ,\ E F\ a n d\ F G` are indicated as `l ,\ b\ a n d\ h` respectively. Indicated the lengths of all other edges.

In /_\ A B C ,\ D ,\ E\ a n d\ F are, respectively, the mid-points of B C ,\ C A\ a n d\ A B . If the lengths of side A B ,\ B C\ a n d\ C A are 7cm, 8cm, and 9cm, respectively, find the perimeter of /_\ D E F.

In figure, A B C is a right triangle right angled at A .\ B C E D ,\ A C F G\ a n d\ AB M N are square on the sides B C ,\ C A\ a n d\ A B respectively. Line segment A X\ _|_D E meets B C at Y . Show that: a r\ (C Y X E)=\ a r\ (A C F G) .

In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\ A C F G\ a n d\ AB M N are square on the sides B C ,\ C A\ a n d\ A B respectively. Line segment A X\ _|_D E meets B C at Ydot Show that: a r(C Y X E)=a r\ (A C F G)

In Figure, the sides B C ,\ C A\ a n d\ A B of a A B C have been produced to D ,\ E\ a n d\ F respectively. If /_A C D=105^0\ a n d\ \ /_E A F=45^0, find all the angles of the \ A B C

In Figure, A B C D is a parallelogram. E\ a n d\ F are the mid-points of the sides A B\ a n d\ C D respectively. Prove that the line segments A F\ a n d\ C E trisect (divide into three equal parts) the diagonal B D .

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 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)

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 D is a parallelogram, E\ a n d\ F are the mid-points of A B\ a n d\ C D respectively. G H is any line intersecting A D ,\ E F\ a n d\ B C at G ,\ P\ a n d\ H respectively. Prove that G P=P H

A B C D is a square E ,\ F ,\ G\ a n d\ H are points on A B ,\ B C ,\ C D\ a n d\ D A respectively, such that A E=B F=C G=D Hdot Prove that E F G H is square.