This question is also based on Similar Triangles

The scale factor for the  top shaded triangle  is  1/4  of ABC

So..its  area  is  scale factor ^2  *  [ ABC]   =  (1/4)^2 * [ABC ]  =  [ ABC ] /16

For the top 1/2 of the figure....the scale factor  is 1/2  of ABC

So...its  area  =   (1/2)^2 [ ABC ]  =  [ ABC ]  / 4    =  (1)

For the top 3/4 of the figure....the scale factor is 3/4 of ABC

So ...its area  =  (3/4)^2 [ ABC ]  = [ABC] *(9/16)  =   (2)

So....the bottom shaded area  = (2) - (1)  =  [9/16 - 1/4] [ABC ] =

[5/16] [ ABC] 

So....the total of the shaded ares  =   [ ABC ] / 16  +  [5/16] [ABC ] =  

[ 6/16] [ ABC ]  =

[3/8] [ ABC]

Thank you again, Chris