In Figure, `A B C D` is a quadrilateral and `B E|A C` and also `B E` meets `D C` produced at `Edot` Show that area of ` A D E` is equal to the area of the quadrilateral `A B C D`

In Figure, compute the area of quadrilateral A B C D Figure

A B C D is a cyclic quadrilateral. A Ba n dD C are produced to meet in Edot Prove that E B C-E D Adot

In Figure, A B C D E is a pentagon. A line through B parallel to A C meets D C produced at Fdot Show that a r( A C B)=a r( A C F) (ii) a r( A E D F)=a r(A B C D E)

In Figure, A B C D E\ is a pentagon. A line through B parallel to A C meets D C produced at Fdot Show that: a r\ ( A C B)=a r\ ( A C F) a r\ (A E D F)=a r\ (A B C D E)

E , F , G , H are respectively, the mid-points of the sides A B ,B C ,C D and D A of parallelogram A B C D . Show that the quadrilateral E F G H is a parallelogram and that its area is half the area of the parallelogram, A B C Ddot GIVEN : A quadrilateral A B C D in which L ,F ,G ,H are respectively the mid-points of the sides A B ,B C ,C D and D Adot TO PROVE : (i) Quadrilateral E F G H is a parallelogram a r(^(gm)E F G H)=1/2a r(^(gm)A B C D) CONSTRUCTION : Join A C and H F

If the diagonals A C ,B D of a quadrilateral A B C D , intersect at O , and seqarate the quadrilateral into four triangles of equal area, show that quadrilateral A B C D is a parallelogram. GIVEN : A quadrilateral A B C D such that its diagonals A C and B D intersect at O and separate it into four parts such that a r( A O B)=a r( B O C)=a r( C O D)=a r( A O D) TO PROVE : Quadrilateral A B C D is a parallelogram.

A B C D is a quadrilateral. A line through D , parallel to A C , meets B C produced in P as shown in Figure. Prove that a r\ ( A B P)=a r\ (Q u a ddotA B C D)dot

In Figure, A B C D is a rectangle in which diagonal A C is produced to Edot If /_E C D=146^0, find /_A O B

The diagonals of quadrilateral A B C D ,A C and B D intersect in Odot Prove that if B O=O D , the triangles A B C and A D C are equal in area. GIVEN : A quadrilateral A B C E in which its diagonals A C and B D intersect at O such that B O = O Ddot TO PROVE : a r( A B C)=a r( A D C)

In Figure, A B C D is a quadrilateral in which diagonal \ A C=84\ c m ; D L_|_A C ,\ B M_|_A C ,\ D L=16. 5\ c m and B M=12\ c m . Find the area of quadrilateral A B C Ddot