CBSE 9th Mathematics Worksheet- Areas of Parallelograms and Triangles

Answer the following

1. Prove that parallelograms on the same base and between the same parallels are equal in area.
2. PQRS and ABRS are parallelograms and X is any point on side BR. Show that : 

         (i) area PQRS = area ABRS
        (ii) area AXS = ½ area PQRS.

      3. In the figure, M is a point in the interior of a parallelogram PQRS. Show that

       

     

4. In the figure, diagonals AC and BD of quadrilateral ABCD intersect at O, such that OB = OD. If AB = CD, show that

i)ar (DOC) = ar (AOB)
ii)ar (DCB) = ar (ACB)
iii)ABCD is a parallelogram.

     

       5. In given figure ABCD, DCFE and ABFE are parallelogram show that ar (ADE) = ar (BCF)

       6. Parallelogram ABCD and rectangle ABEF are on the same base and have equal areas. Show that perimeter of the parallelogram is greater than that of rectangle  

  7. P and Q are mid-points of sides AB and AC respectively. Of triangle ABC. R is mid-point of AP, prove that:

           1 ) ar(PRQ)=1/2 ar(ARC)

           2 ) ar(RQC)=3/8 ar(ABC)

           3 ) ar(PBQ)=ar(ARC)

8. In adjoining figure ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that

                                

                               

9. D, E & F are mid points of sides of triangle BC, CA & AB respectively. Show
   that
                       

        10. In given figure ABCD is a quadrilateral and BE||AC is such that BE meets at E on
the extended CD. Show that area of triangle ADE is equal to the area of quadrilateral ABCD.

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