SOLUTION: One side of a parallelogram is 10cm and its diagonals are 16m and 24cm respectively. Find its area

1.  The area of a parallelogram is equal to half the product of its diagonals by the sine of the angle between them:

    S = .

    See the lesson Area of a parallelogram in this site.

    Any of the two angles is good.


2.  You have the diagonals, and all you need is the sine of the angle between the diagonals.

    Instead of sine, we can find the cosine of the angle between the diagonals.

    For it, we will use the Cosine Law by applying it to the triangle formed by halves of diagonals and the side of the parallelogram:

     = .

    Which gives   =  = .

    And then  =  =  =  =  =  =  =  = .


4.  Finally, the area of the parallelogram is

    S =  =  = 58.095  (approximately).


Answer.  The area of the parallelogram is   = 58.095  (approximately).