+1713 We have triangle △ ABC where AB=AC and AD is an altitude. Meanwhile, E isa point on AC such that AB ∥DE. If BC = 12 and the area of△ABC is 180, what is the area of ABDE?
Thank you in advance,
tommarvoloriddle
+9488 This diagram has more information than I showed how to find. If you're unsure how to find, for example, AD = 30, and want further explanation, just ask. 
m∠EDC = m∠ABC because corresponding angles are congruent.
m∠ECD = m∠ACB because they are the same angle
So by the AA similarity theorem, △EDC ~ △ABC
When we draw a height to the base of an isosceles triangle, we split the base exactly in half.
So the scale factor from △ABC to △EDC is 1/2. And so...
area of △EDC = ( 1/2 )( 1/2 )( area of △ABC)
area of ABDE = area of △ABC - area of △EDC
area of ABDE = 180 - ( 1/2 )( 1/2 )( 180 )
area of ABDE = 180 - 45
area of ABDE = 135
The areas are in square units.
