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.

Question

Philoid · Accepted Answer

Given: BE ||AC

We know that any two or more Triangles having the same base and lying between the same parallel lines are equal in area.

∴ Area (Δ ACE) = Area (Δ ACB) –1

Add Area (Δ ADC) on both sides of eq –1

We get,

Area (Δ ACE) + Area (Δ ADC) = Area (Δ ACB) + Area (Δ ADC)

That is,

Area (Δ ADE) = Area (quad. ABCD)