`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 ,\ 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 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

A B C D is a parallelogram in which B C is produced to E such that C E=B CdotA E intersects C D\ at Fdot 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 ^(gm) ABCD

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 Q 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 GIVEN : A A B C ,D is the mid-point of B C and E is the mid-point of the median A Ddot TO PROVE : a r( B E D)=1/4a r( A B C)dot

D is the mid-point of side B C of A B C and E is the mid-point of B Ddot If O is the mid-point of A E , prove that a r( B O E)=1/8a r( 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 .

A B C D is a parallelogram, G is the point on A B such that A G=2\ G B ,\ E\ is a point of D C such that C E=2D E\ a n d\ F is the point of B C such that B F=2F Cdot Prove that: a r\ (\ E B G)=a r\ (\ E F C)

A B C D is a parallelogram, G is the point on A B such that A G=2\ G B ,\ E\ is a point of D C such that C E=2D E\ a n d\ F is the point of B C such that B F=2F Cdot Prove that: Find what portion of the area of parallelogram is the area of \ E F G

A B C D is a parallelogram, G is the point on A B such that A G=2\ G B ,\ E\ is a point of D C such that C E=2D E\ a n d\ F is the point of B C such that B F=2F Cdot Prove that: a r\ (\ E F C)=1/2\ a r\ (\ E B F)