Answer:
168 cm²
Explanation:
... ADBC = (1/2)AABC because DC is a median of ∆ABC.
... ADEC = ADEB = (1/2)ADBC because DE is a median of ∆BDC.
... ADEF = (1/2)ADEB because DF is a median of ∆BDE.
The given area is the sum of two of the areas described above:
... ADCF = ADEC + ADEF
... ADCF = (1/2)ABDC +(1/2)ADEB . . . . substitute from above
... = (1/2)(1/2)AABC + (1/2)(1/2)(1/2)AABC . . . . more substitution
... = (3/8)AABC
Multiplying by 8/3 gives ...
... AABC = (8/3)ADCF = (8/3)×(63 cm²)
... AABC = 168 cm²
