`A B C D` is a parallelogram and `O` is any point in its interior. Prove that:
(i) `a r\ ( A O B)+a r\ (C O D)=1/2\ a r(A B C D)`
(ii) `a r\ ( A O B)+\ a r\ ( C O D)=\ a r\ ( B O C)+\ a r( A O D)`

In Figure, A B C D is a parallelogram and E F C D is a rectangle. Also A L\ _|_D C . Prove that (i) a r(A B C D=a r(E F C D) (ii) a r\ ( A B C D)=D C x A L

In Figure, P is a point in the interior of a parallelogram A B C Ddot Show that a r( A P B)+a r( P C D)=1/2a r\ (|""|^(gm)A B C D) a r\ ( A P D)+a r\ ( P B C)=a r\ ( A P B)+a r( P C D)

In Figure, P is a point in the interior of a parallelogram A B C D . Show that a r( A P B)+a r( P C D)=1/2a r(^(gm)A B C D) a R(A P D)+a r( P B C)=a r( A P B)+a r( P C D)

If A B C D is a parallelogram, then prove that a r\ (/_\\ A B D)=\ a r\ (/_\\ B C D)=\ a r\ (/_\\ A B C)=\ a r\ (/_\\ A C D) = 1/2\ a r\ (para l l e l o g r a m A B C D)

A B C D is a parallelogram whose diagonals intersect at O . If P is any point on B O , prove that: a r\ (triangle \ A B P)=\ a r\ (triangle \ C B P)

O is any point on the diagonal B D of the parallelogram A B C D . Prove that a r( /_\O A B)=a r( /_\O B C)

A B C D is a trapezium in which AB is parallel to CD . The diagonals A C and B D intersect at O . Prove that (i) A O B ~ C O D (ii) If O A=6c m , O C=8c m , Find: (A r e a\ ( A O B))/(A r e a\ ( C O D)) (b) (A r e a\ ( A O D))/(A r e a\ ( C O D))

A point O inside a rectangle A B C D is joined to the vertices. Prove that the sum of the areas of a pair of opposite triangles so formed is equal to the sum of the other pair of triangles. Given: A rectangle A B C D\ a n d\ O is a point inside it. O A ,\ O B ,\ O C\ a n d\ O D have been joined. To Prove: a r\ (A O D)+\ a r\ ( B O C)=\ a r\ ( A O B)+\ a r( C O D)

If A B C D is a parallelogram, the prove that a r( A B D)=a r( B C D)=a r( A B C)=a r( A C D) =1/2a r (||^(gm) A B C D)

A B C D is a rectangle with O as any point in its interior. If a r\ ( A O D)=3\ c m^2a n d\ a r\ ( B O C)=6\ c m^2, then area of rectangle A B C D is: 9c m^2 (b) 12\ c m^2 (c) 15 c m^2 (d) 18\ c m^2