Question

In fig ABCD is a quadrilateral and BE parallel AC and also BE meets DC produced at E show that area of triangle ADE is equal to the area of the quadrilateral ABCD

Answer 1

Solution :-

Please see the attachment.

Given that BE II AC

⇒ ABEC is a parallelogram, of which opposite sides are parallel.

Δ ABC and Δ ACE lie on the same base AC and between the same parallel AC and BE.

∴ Area(Δ ABC) = Area(Δ ACE)

By adding area(Δ ADC) to both sides

⇒ Area(Δ ABC) + Area(Δ ADC) = Area(Δ ACE) + Area(Δ ADC)

⇒ Area (Parallelogram ABCD) = Area(Δ ADE)

Hence, proved.

Answer. 

Answer 2

Hi friend..
See the attached file

I hope it will help you

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