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In right $\triangle ABC$, shown here, $AB = 15 \text{ units}$, $AC = 28 \text{ units}$ and points $D,$ $E,$ and $F$ are the midpoints of $\overline{AC}, \overline{AB}$ and $\overline{BC}$, respectively. In square units, what is the area of $\triangle DEF$?

 

 Mar 22, 2021
 #1
avatar+117635 
+1

Triangle ABC  and  FDE are similar

 

Scale  factor  of  DEF  to  ABC = 1/2

 

Area of ABC  =  AC * AB  / 2  =  28 * 15  / 2  =   210 units^2

 

Area of   DEF = 

 

Area of  ABC  * (scale factor)^2  =    210  *  (1/2)^2  =  210 / 4  =  52.5 units^2

 

 

cool cool cool

 Mar 22, 2021
 #2
avatar+1164 
+4

Area of ΔDEF = 1/8(AB * AC)

 Mar 22, 2021

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