In a rectangle `A B C D ,\ \ A B=20 c m ,\ \ /_B A C=60o` , calculate side `B C` and diagonals `A C` and `B D` .

A paper is in the form of a rectangle A B C D in which A B=20\ c m and B C=14\ c mdot A semicircular portion with B C as diameter is cut off. Find the area of the remaining part.

The diagonals of a rectangle A B C D\ meet at O . If /_B O C=44^0, find /_O A D

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 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 Figure, A B C D is a trapezium in which A B C D and A D=B Cdot show that : /_A=/_B (ii) /_C=/_D A B C~= B A D diagonal A C=d i agon a lB D

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.

If A B C D is a rectangle with /_B A C=32^0, find the measure of /_D B C

In a A B C , A D is the bisector of /_A , meeting side B C at D . If A B=10 c m , A C=14 c m and B C=6c m , find B D and D C (ii) If A C=4. 2 c m , D C=6c m and B C=10 c m , find A B . (iii) If A B=5. 6 c m , A C=6c m and D C=3c m , find B C .

In a A B C , A D is the bisector of /_A , meeting side B C at D . If A D=5. 6 c m , B C=6c m and B D=3. 2 c m , find A C . (ii) If A B=10 c m , A C=6c m and B C=12 c m , find B D and D C .

In Figure, A B C D is a trapezium in which A B=7c m ,\ A D=B C=5c m ,\ D C=x\ c m , and distance between A B\ a n d\ D C is 4c m . Find the value of x and area of trapezium A B C D