We have triangle ABC where AB = AC and AD is an altitude. Meanwhile, E is a point on AC such that AB is parallel to DE. If BC = 15 and the area of triangle ABC is 200, what is the area of ABDE?
We have triangle ABC where AB = AC and AD is an altitude. Meanwhile, E is a point on AC such that AB is parallel to DE. If BC = 15 and the area of triangle ABC is 200, what is the area of ABDE?
[ABDE] = 3/4[ABC]
Area ABC = (1/2) BC * AD
200 = (1/2) 15 * AD
400 = 15 * AD
400 / 15 = AD
80/3 = AD
See the following image :
Since AB is parallel to DE.....triangle EDC is similar to triangle ABC
And DC and BC are corresponding sides
Sinc AB = AC....then AD bisects BC...so
DC =(1/2) BC
So the scale factor of EDC to ABC = 1/2
So the area of EDC to ABC = (scale factor)^2 (area of ABC ) = (1/4) (200) = 50 = [EDC ]
So [ ABDE ] = [ ABC ] - [EDC ] = 200 - 50 = 150