Question

ABCD is a quadrilateral and BE parallel to AC and also BE meets DC produced at E.Show that the 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