In triangle ABC, point D divides side AC so that AD : DC = 1 : 2. Let E be the midpoint of BD and let F be the point of intersection of line BC and line AE. Given that the area of ΔABC is 360 cm2, what is the area of ΔAED?
Triangles BDA and BDC are under the same height...so....their areas are to each other as their bases
So area of BDA = (1/(1 + 2)) [ABC] = (1/3) [360] = 120
Note that sin angle BEA = sin angle DEA
And BE = ED
And AE= AE
So
area of triangle BEA = (1/2) (BE)(AE) sin (BEA)
area of triangle AED = (1/2) (ED)(AE) sin ( DEA)
So area of triangle BEA = area of trinangle AED
So
[AED] + [ BEA ] = [ BDA ]
2 [ AED ] = 120
[ AED ] = 60