In the figure ABCD is a parallelogram where AL CD and CM AD. To calculate area of this parallelogrami if we consider the base as CD then the corresponding height will be AL because AL CD, but if we take base as AD then the corresponding height will be CM because CM AD. Thus

Area of parallelogram ABCD = Base X height

                                                      = AD X CM

                                                      = CD X AL

Given      A parallelogram ABCD in which AB is the base and AL the corresponding altitude.

To prove    

Construction     Draw BM  produced DC to M. Now   is a rectangle.

Proof   Since   and rectangle    are on the same base and between the same parallels.

                                          [  The area of Rectangle = Base X Height ]

Hence,        

Area of paralleogram ABCD = DC × AL  (Taking base as DC and Height as AL )

Area of paralleogram ABCD = AB × AL (AB = DC as opposite side of the parallelogram are equal)

Therefore,

Area of paralleogram ABCD = 14 × 10 ……(1)

Taking the base of Parallelogram ABCD as AD the height will be CM

Area of paralleogram ABCD = AD × CM (taking base as AD and height as CM)

Area of paralleogram ABCD = AD × 7 ……(2)

Since equation 1 and 2 both represent the Area of the same Parallelogram ABCD , both should be equal.

Hence from equation (1) and (2),

This means that,

  14 X 10 = AD X 7

  AD X 7 = 14 X 10