In the diagram below, \(BE=EC=DF,\) and \(\triangle ADF\) has the same area as \(\triangle DEF.\) If rectangle \(DXYF\) has area 42 what is the area of \(\triangle ABC\)? 
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+506 Notice that ABC can be divided into 4 congruent triangles (specifically triangles ADF, BDE, DEF, and EFC). We just need to find the area of one of these triangles and multiply by 4.
Also notice that DEF is half the area of DXYF. Therefore, the area of ABC is equal to \(\frac{42}{2} \cdot 4 = \boxed{84}\)
+506 Notice that ABC can be divided into 4 congruent triangles (specifically triangles ADF, BDE, DEF, and EFC). We just need to find the area of one of these triangles and multiply by 4.
Also notice that DEF is half the area of DXYF. Therefore, the area of ABC is equal to \(\frac{42}{2} \cdot 4 = \boxed{84}\)
