Lines
A
D
,
B
E
,
and
C
F
are medians of triangle
A
B
C
, and the yellow area is
4
7
, how much is the blue area?
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Medians divide the triangle in six triangles of the same area. The yellow area covers two of the six triangles of the same area ∴ the blue area is twice than yellow area ⇒ the blue area is 4 7 × 2 = 9 4
△ A O B and △ A C B have the same base, A B , and their heights are in proportion 3 : 1 since C F = 3 × O F .
Area [ A B C ] = 3 × [ A O B ]
[ b l u e ] = [ A B C ] − [ A O B ] = 2 × [ A O B ] = 2 × 4 7 = 9 4
Actually medians divide △ A B C into six triangles of equal area, in this case four of them are blue and two yellow.
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The three medians divide the triangle into six smaller triangles of equal area. Since the yellow area has 2 triangles, the area of one triangle is 2 4 7 = 2 3 . 5 . The blue area has 4 triangles, so the area of the blue area is 4 ( 2 3 . 5 ) = 9 4