Question (1 Viewer)

[hunterbear]

F and E are midpoints of the sides AB and AC respectively in a triangle ABC. X and Y are points on the side BC such that EX and FY are parallel. Show that parallelogram EFYX has half the area of triangle ABC.

 

[Drongoski]

area of ABC = 4 x area of AFE

triangle FEX has height = height of triangle AFE relative to common base FE

.: area of FEX = area of AFE

.: area of //gram EFYX = 2 x area of FEX = 2 x area of AFE = half of area of triangle ABC.

 

[hunterbear]

Thanks!