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Point E is the midpoint of the side BC of triangle ABC and F is the midpoint of AE. The line through BF intersects AC at D. Find the area, in cm squared, of triangle AFD if the area of the triangle is 48 cm2

 Jan 11, 2020
 #1
avatar+109739 
-1

See the following image  :

 

 

 

Note that triangles BEF and BGD  are similar

So

EF/BE = GD/BG

4/6 = GD/8

GD = 8*4/6 = 32/6  = 16/3

And GD is the altitude of triangle BDC

And the area of this triangle  = (1/2)(BG)(GD)  = (1/2)(8)(16/3)  = 64/3 units^2     (1)

And the area of triangle BFA  = area of triangle  BEA  - area of triangle BEF  = 

Area of triangle BEA = 24

Area of triangle BEF = (1/2) of area of triangle BEA   =12

So area of triangle BFA  =24 - 12  =12

 

So....  area of triangle AFD  = 

Area of triangle ABC  - area of triangle BDC  - area of triangle BFA =  48 - 64/3 - 12  = 36 - 64/3  =

[108 -64] / 3  =   44/3  units^2

 

cool cool cool

 Jan 11, 2020
 #2
avatar+531 
+3

Your concept is good, but the answer is wrong!

You did not subtract the area of a triangle  CDG.

The area of AFD = 4 cm²   indecision

Dragan  Jan 11, 2020
edited by Dragan  Jan 11, 2020
edited by Dragan  Jan 11, 2020
edited by Dragan  Mar 21, 2020
 #3
avatar+11729 
+3

Point E is the midpoint of the side BC of triangle ABC and F is the midpoint of AE. The line through BF intersects AC at D. Find the area, in cm squared, of triangle AFD if the area of the triangle is 48 cm2

 

laugh

 Jan 11, 2020

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