Area of similar triangle Theorem:If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.
We have, ⇒DE|BC ⇒ar(△ADE)=ar(△ trap.DEBC ) ⇒ar(△ADE)=ar(△ABC)−ar(△ADE) ⇒2ar(△ADE)=ar(△ABC) In In △ADE and △ABC ⇒∠A=∠A common] ⇒∠ADE=∠ABC [corresponding angles ] ⇒△ADE∼△ABC[ by AA similarity ] Byarea of similar triangle theorem ⇒