In Fig. 9.22, ABCD is a quadrilateral and `B E\ ||\ A C`and also BE meets DC produced at E. Show that area of `DeltaA D E`is equal to the area of the quadrilateral ABCD.

Explanation

Lets proof BE||AC and take other things given.

area(ABCD)=area(ACD)+area(ABC)

area(ADE)=area(ACD)+area(AEC)

So, area(ABC)=area(AEC)

According theorem 9.2

BE||AC.