A parallelogram is a quadrilateral whose opposite sides are equal length and parallel. The diagonals of a parallelogram are unequal and bisect each other. If  is a parallelogram then its area can be calculated in two ways:

(a) When the base and height are given:
            Since,  is a parallelogram with base,  and height,

 Area of the parallelogram  Area of the rectangle
   
           (as)
   
 Area of parallelogram  base  height

(b) When adjacent sides and their included angle is given:
            Since,  is a parallelogram. Take  and  as its two adjacent sides with included angle .

 Area of parallelogram
            But
            Or
            Or
 Area of  
 Area of Parallelogram  Product of adjacent sides

Example:
            Find the base of a parallelogram whose area is square cm and height cm.
Solution:
            Since, area square cm
            height cm 
             Area of parallelogram  base  height
             base
            Base cm.

Example:
            Find the area of a parallelogram, two adjacent sides of which are cm and cm and their included angle is.
Solution:
            Here, one side, cm, other side, cm,
             Area
                         
                  &nb sp;      
                  &nb sp;       square cm