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Let ABCD be a square with total area 1600. F is the midpoint of AD and E is the midpoint of FD.  BE and CF intersect at G. Find the area of triangle EFG.

 

 May 5, 2020
 #1
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The  sides  =  40

 

FD   = 20...so.....FE  = 10

 

Note  that triangle BGC  is similar to triangle FGE

 

The  base  of triangle  FGE  =  (1/4)   of  base of triangle FGE

 

So...the  height  of  triangle FGE  = must  be (1/4)  the  height of  triangle BGC

 

So  height of BGC   = 4 times height of FGE

 

So....

 

height of FGE  + 4 *height of FGE  = side length  =   40

 

5 *height FGE   = 40

 

height of FGE  =40/5  =  8

 

 

So  the area of triangle FGE  =(1/2) FE * 8    =  (1/2) (10)(8)  =   40

 

 

cool cool cool

 May 5, 2020

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