Question

ABC point D is the midpoint of AB , point E is the midpoint of BC , and point F is the midpoint of BE . Find area of △ABC, if ADCF= 63 cm2

Answer 1

168 cm²

Step-by-step 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