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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.

 Jan 23, 2024
 #1
avatar+129881 
+1

                                             A

 

                            E                      D

                                  T

                B                         M                  C

 

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

 

cool cool cool

 Jan 24, 2024
edited by CPhill  May 28, 2024

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