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Point D is the midpoint of median AM of triangle ABC. Point E is the midpoint of AB, and point T is the intersection of BD and ME. Find the area of triangle BEC if [ABC] = 14.

 Jun 17, 2024
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Height of ABC  =  AM

Base of ABC = BC

 

\([ ABC ]  = (1/2) (BC) (AM) =  14   → (BC) (AM)  =  28 \)

Height of BEC   = (1/2)AM

Base of BEC =  BC

 

\([ BEC ]  = (1/2) (BC) (1/2)AM =  (1/4)(BC) (AM)  =  (1/4) (28)  =  7\)

 

So our final answer is 7. 

 

Thanks! :)

 Jun 17, 2024
edited by NotThatSmart  Jun 17, 2024

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