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In triangle ABC, point D divides side AC so that AD : DC = 1 : 2. Let E be the midpoint of BD and let F be the point of intersection of line BC and line AE. Given that the area of ΔABC is 360 cm2, what is the area of ΔAED?

 

 Jun 15, 2022
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Triangles BDA and BDC are under the same height...so....their areas are to each other as their bases

 

So   area of   BDA =  (1/(1 + 2)) [ABC]  = (1/3) [360] = 120

 

Note that sin  angle BEA =  sin angle DEA

And  BE = ED

And AE= AE

 

So

area of  triangle  BEA = (1/2) (BE)(AE) sin (BEA)

area of triangle  AED =  (1/2) (ED)(AE) sin ( DEA)

 

So  area of  triangle  BEA  = area of trinangle  AED  

 

So

 

[AED] + [ BEA ]  = [ BDA ] 

 

 2 [ AED ] =   120

 

[ AED ]  =   60

 

 

cool cool cool

 Jun 15, 2022
edited by CPhill  Jun 15, 2022
edited by CPhill  Jun 15, 2022

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