+0  
 
0
39
1
avatar+417 

In triangle $ABC$, we have that $E$ and $F$ are midpoints of sides $\overline{AC}$ and $\overline{AB}$, respectively. The area of $\triangle ABC$ is 24 square units. How many square units are in the area of $\triangle CEF$?

michaelcai  Nov 12, 2017
Sort: 

1+0 Answers

 #1
avatar+78762 
+1

Call AB  the height of  ΔABC and AC the base

 

Then  (1/2) AC * AB  =  24 units^2   ⇒  AC * AB  =  48 units^2

 

But   EC = (1/2)AC  is the base of   ΔCEF  and (1/2)AB =  AF  is the height

 

So  area of    Δ CEF  =  (1/2)CE *AF  =  (1/2) [(1/2)AC] * [(1/2)AB]   =  1/8 AC * AB  =

 

(1/8)* 48  =   6 units^2

 

 

cool cool cool

CPhill  Nov 12, 2017

5 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details