We have triangle ABC where AB = AC and AD is an altitude. Meanwhile, E is a point on AC such that AB and DE are parallel. If BC=12 and the area of ABC is 180 what is the area of ABDE?

Guest Aug 21, 2019

#1**+1 **

See the following image :

Since DE is parallel to AB, the triangle DEC is similar to triangle BAC

And BC = 12 and DC = 6

So the base of triangle DEC is 1/2 that of triangle BAC

So....the scale factor of triangle DEC to triangle BAC = 1/2

So....the area of triangle DEC = (scale factor)^2 * (area of triangle BAC) =

(1/2)^2 * (180) = (1/4) (180) = 45

So...the area of ABDE = area of triagle BAC - area of triangle DEC = 180 - 45 = 135

CPhill Aug 21, 2019