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?
+128407 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
