Let G be the center of gravity of the triangle, GA = 2 times the root 3, GB = 2 times the root 2, GC = 2, and find the area of the triangle ABC

Let the extension of Ag intersect BC at D,
Because G is the center of gravity
So BD = CD
Because BG = CG = 2
Therefore, according to the property of "three lines in one", we get GD ⊥ BC
According to the nature of the center of gravity, "the center of gravity of triangle divides each center line into two parts of 1:2", we know that GD = Ag / 2 = √ 3
So according to Pythagorean theorem, BD = 1
So BC = 2
And ad = 3 √ 3
So s △ ABC = BC * ad / 2
＝2*3√3/2＝3√3

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