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Question is based on Similar Triangles

 

shreyas1  Oct 15, 2018
 #1
avatar+90968 
+1

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]

 

cool cool cool

CPhill  Oct 15, 2018
 #2
avatar+462 
+1

Thank you again, Chris 

shreyas1  Oct 16, 2018

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