Question

In the given figure, ABCD is a quadrilateral and BE || AC and also BE meets DC produced at E. Show that the area of ∆ADE is equal to the area of quad. ABCD.

Answer 1

∆BAC and ​∆EAC lie on the same base AC and between the same parallel lines.
So, ar(∆BAC) = ​ar(∆EAC)
Adding ​ar(∆ADC) on both sides, we get:
⇒ ​ar(∆BAC) + ​ar(∆ADC) = ​ar(∆EAC) + ​ar(∆ADC)
⇒ ar(quad. ABCD) = ar(​​∆ADE)
Hence, proved.